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Why the universe cannot logically be infinite in time backwards

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File:Wooden hourglass 3.jpg
passage of time, imaged/S. Sepp

Further to “No Big Bang: Universe Always Was” just posted by Donald McLaughlin, Ashby Camp gave Uncommon Descent permission to post these notes from a class he taught at the 2018 Harding University Bible Lectureship titled “Answering the New Atheism.” Worth pondering:


1.The second premise of the Kalam cosmological argument is: The universe began to exist. It is more reasonable to believe this is true than to deny it because, Scripture aside, there are strong philosophical and scientific reasons for believing it.

a. The philosophical argument for the universe having a beginning is that past time cannot be infinite because an infinite amount of time cannot already have been exhausted so as to arrive at the present. Infinite time is limitless, inexhaustible, and thus cannot have been exhausted.

(1) Put differently, one could never traverse an infinite sequence of time units, an infinite number of seconds, minutes, hours, etc., to arrive at now. There always would be more time units to traverse before now. If one begins counting down from minus infinity, one cannot count to the present. An infinite amount of time can never pass because it is limitless; it can only be in process, never complete. To quote the New Dictionary of Christian Apologetics, (p. 700), “One can neither count from one to infinity nor count down from infinity to one. There is always an infinite distance to travel, so one never arrives.”

(2) Sean McDowell and Jonathan Morrow make the point this way in Is God Just a Human Invention? (Grand Rapids: Kregel Publications, 2010), 75-76:

Imagine you went for a walk in the park and stumbled across someone proclaiming aloud, “… five, four, three, two, one—there, I finally finished! I just counted down from infinity!” What would be your initial thought? Would you wonder how long the person had been counting? Probably not. More likely, you would be in utter disbelief. Why? Because you know that such a task cannot be done. Just as it’s impossible to count up to infinity from the present moment, it’s equally impossible to count down from … infinity to the present moment. Counting to infinity is impossible because there is always (at least) one more number to count. In fact, every time you count a number, you still have infinite more to go, and thus get no closer to your goal. Similarly, counting down from infinity to the present moment is equally impossible. Such a task can’t even get started! Any point you pick in the past to begin, no matter how remote, would always require (at least) one more number to count before you could start there. Any beginning point would require an infinite number of previous points. Here’s the bottom line: we could never get to the present moment if we had to cross an actual infinite number of moments in the past. Yet, since the present moment is real, it must have been preceded by a finite past that includes a beginning or first event. Therefore, the universe had a beginning.

(3) The impossibility of infinite past time, of having already traversed an infinite timespan, does not mean that future time will not go on forever. Future time is potentially not actually infinite. In other words, it is infinity in progress, something that will move toward infinity but never arrive; you’ll never get to the end of it. So it poses no problem like the claim of having already traversed an infinite timespan.

(4) The impossibility of traversing an infinite timespan, an infinite sequence of time units, need not mean that God has not always existed. There are ways of dealing with God’s relationship to time so that he does not exist (or has not always existed) in a sequence of individuated moments, a sequence of time units. His eternality is not one of infinite time but one of either timelessness or a different kind of time that has no measure or metric. For example, William Lane Craig’s view is that “God is timeless without creation and temporal since creation.” Philosophers Alan Padgett and Richard Swinburne refer to time before creation as “metrically amorphous time,” meaning it differs from our “measured time” (see, e.g., Eternity in Christian Thought).

(5) This philosophical claim that the universe cannot always have existed makes sense to me and to many philosophers, but there are others who are not persuaded.

(a) Some, for example, point to the fact a finite timespan, say one minute, can be subdivided infinitely into units of decreasing length, and yet one can still traverse that timespan. The claim is that in going from 0 to 1 minute one traverses an infinite number of time units to arrive at 1 minute, so it is not true that one cannot traverse an infinite number of time units to arrive at the present. But there is a problem with that claim. The subdivisions of a finite timespan are only potentially infinite in number. It is true that one could keep subdividing forever, but each further subdivision results in a finite number of subdivisions the sum of which is the finite timespan being subdivided. The number of subdivisions can grow toward an infinite number but can never actually reach an infinite number. Whereas, when speaking of an infinite timespan one is speaking of an actually infinite set of time units, the sum of which is an infinite length of time.

(b) Though this philosophical claim that the universe necessarily began to exist continues to be debated, it dovetails nicely with the scientific acceptance of the universe having a beginning. That is the subject to which I now turn.

  

Readers?

329 Replies to “Why the universe cannot logically be infinite in time backwards

  1. 1
    asauber says:

    The concept of Infinity is useful in mathematics, so a previous discussion here at UD I was involved in informs me. This version of Infinity applies to the realm of imagination.

    In the physical realm, Infinity is an absurdity. It doesn’t apply to anything.

    Andrew

  2. 2
    Jim Thibodeau says:

    wikipedia:

    The ancient philosopher Aristotle argued that the world must have existed from eternity in his Physics as follows. In Book I, he argues that everything that comes into existence does so from a substratum. Therefore, if the underlying matter of the universe came into existence, it would come into existence from a substratum. But the nature of matter is precisely to be the substratum from which other things arise. Consequently, the underlying matter of the universe could have come into existence only from an already existing matter exactly like itself; to assume that the underlying matter of the universe came into existence would require assuming that an underlying matter already existed. As this assumption is self-contradictory, Aristotle argued, matter must be eternal.

  3. 3
    Seversky says:

    One of the things kf and I agree on is that, since something cannot come from nothing and there is something then there must have always been something, although not necessarily in the form of this universe.

  4. 4
    Belfast says:

    @3
    Something cannot NATURALLY come from nothing.

  5. 5
    kairosfocus says:

    AS, infinity –better, the transfinite — is relevant, through the hyperreals. Take some H larger than any number we can count to, and do h = 1/H, a number smaller than any 1/n, where n is a number we can count to. This helps us establish tamed infinitesimals, thus Calculus through non-standard analysis. There is thus a cloud of infinitesimals around 0, and this can be extended by addition around any r mileposted by numbers we can count to n. This allows us to do analysis on the continuum. H also allows us to address the issue of a claimed or implicit infinite quasi-physical past joined to now by finite stage, causal temporal, thermodynamically regulated, energy flow constrained succession of stages [“years” for convenience]. Such cannot be transfinite, as no stepwise, finite stage process can bridge the transfinite. -H, -H+1, -H+2, . . . will always see some (-H+k) –> K, K+1, K+2 etc, which will always be in finite stage succession from H then K, i.e. we have no good reason to imagine we can so traverse the span to a 0-point such as the Bang, from which we can count up to now, what ~14 bn y on the usual timeline? So, an infinite quasi physical past is implausible. Similarly, we do not have circular causation where some now causes its antecedents. We see a finitely remote beginning of our observed cosmos and any substrate behind it. This is where we need causally adequate necessary being to account for our world, and given our moral government [including of our rationality] we face a need for an inherently good, utterly wise necessary being capable of being the root of worlds fine tuned for C-chem, aqueous medium, terrestrial planet, cell based life. Which should sound familiar. KF

  6. 6
    groovamos says:

    One of the things kf and I agree on is that, since something cannot come from nothing and there is something then there must have always been something, although not necessarily in the form of this universe.

    Yes, yes, thank you for that. The every day ‘something’ (experienced by everyone) is nature itself. The primary ‘something’ that is the source of nature, by any logical reasoning is superior to nature, the definition of ‘supernatural’. And readily experience by those with the requisite dispostion and effort.

  7. 7
    kairosfocus says:

    F/N: Isa 55:

    >>
    Seek the Lord while He may be found;
    Call on Him [for salvation] while He is near.
    7

    Let the wicked leave (behind) his way
    And the unrighteous man his thoughts;
    And let him return to the Lord,
    And He will have compassion (mercy) on him,
    And to our God,
    For He will abundantly pardon.
    8

    “For My thoughts are not your thoughts,
    Nor are your ways My ways,” declares the Lord.
    9

    “For as the heavens are higher than the earth,
    So are My ways higher than your ways
    And My thoughts higher than your thoughts.
    10

    “For as the rain and snow come down from heaven,
    And do not return there without watering the earth,
    Making it bear and sprout,
    And providing seed to the sower and bread to the eater,
    11

    So will My word be which goes out of My mouth;
    It will not return to Me void (useless, without result),
    Without accomplishing what I desire,
    And without succeeding in the matter for which I sent it.>>

    KF

  8. 8
    Fasteddious says:

    Regarding God’s time, it is conceivable that God has a different timeline than we do. This can be explained by assuming that we are a simulation, and God is the simulator. The simulator has his own time line, while the simulation time line only begins when the simulator starts the simulation. Moreover, the simulator’s timeline can flow at a totally different rate from ours; e.g. when humans simulate a nuclear explosion, the time steps of picoseconds may take hours to run on the computer. On the other hand, when simulating plate tectonics, thousands of years may take only seconds of computer time. Also, as in a video game, the simulator can suspend the simulation to go off and have lunch, coming back to pick up where it stopped some time later. I explore these concepts and more at: https://thopid.blogspot.com/2019/01/our-simulated-world.html

  9. 9
    bornagain77 says:

    As to this comment from the article,,,

    Why The Universe Cannot Logically Be Infinite In Time Backwards,,,
    one could never traverse an infinite sequence of time units, an infinite number of seconds, minutes, hours, etc., to arrive at now.,,,
    (God’s) eternality is not one of infinite time but one of either timelessness or a different kind of time that has no measure or metric. For example, William Lane Craig’s view is that “God is timeless without creation and temporal since creation.” Philosophers Alan Padgett and Richard Swinburne refer to time before creation as “metrically amorphous time,” meaning it differs from our “measured time” (see, e.g., Eternity in Christian Thought).,,,

    Hmm, so to try “to arrive at now”? And just what is this moment called “now” that is being attived at? As Antoine Suarez put it, “it is impossible for us to be ‘persons’ experiencing ‘now’ if we are nothing but particles flowing in space time.”

    Nothing: God’s new Name – Antoine Suarez – video
    Paraphrased quote: (“it is impossible for us to be ‘persons’ experiencing ‘now’ if we are nothing but particles flowing in space time. Moreover, for us to refer to ourselves as ‘persons’, we cannot refer to space-time as the ultimate substratum upon which everything exists, but must refer to a Person who is not bound by space time. i.e. We must refer to God!”)
    https://www.youtube.com/watch?v=SOr9QqyaLlA

    There simply is no moment called ‘now’ for ‘particles flowing in space time’.

    As Stanley Jaki put it, “There can be no active mind without its sensing its existence in the moment called now.,,, ,,,There is no physical parallel to the mind’s ability to extend from its position in the momentary present to its past moments, or in its ability to imagine its future. The mind remains identical with itself while it lives through its momentary nows.”

    The Mind and Its Now – Stanley L. Jaki, May 2008
    Excerpts: There can be no active mind without its sensing its existence in the moment called now.,,,
    Three quarters of a century ago Charles Sherrington, the greatest modern student of the brain, spoke memorably on the mind’s baffling independence of the brain. The mind lives in a self-continued now or rather in the now continued in the self. This life involves the entire brain, some parts of which overlap, others do not.
    ,,,There is no physical parallel to the mind’s ability to extend from its position in the momentary present to its past moments, or in its ability to imagine its future. The mind remains identical with itself while it lives through its momentary nows.
    ,,, the now is immensely richer an experience than any marvelous set of numbers, even if science could give an account of the set of numbers, in terms of energy levels. The now is not a number. It is rather a word, the most decisive of all words. It is through experiencing that word that the mind comes alive and registers all existence around and well beyond.
    ,,, All our moments, all our nows, flow into a personal continuum, of which the supreme form is the NOW which is uncreated, because it simply IS.
    http://metanexus.net/essay/mind-and-its-now

    Simply put, the experience of ‘the now’, and/or the ‘persistence of self identity through time’ is one of the defining attributes of the immaterial mind that cannot be reduced to any possible materialistic explanation, i.e. reduced to ‘particles flowing in space time’.

    The Mind and Materialist Superstition – Michael Egnor – 2008
    Six “conditions of mind” that are irreconcilable with materialism: –
    Excerpt: Intentionality,,, Qualia,,, Persistence of Self-Identity,,, Restricted Access,,, Incorrigibility,,, Free Will,,,
    http://www.evolutionnews.org/2.....13961.html

    Six reasons why you should believe in non-physical minds – 01/30/2014
    1) First-person access to mental properties
    2) Our experience of consciousness implies that we are not our bodies
    3) Persistent self-identity through time
    4) Mental properties cannot be measured like physical objects
    5) Intentionality or About-ness
    6) Free will and personal responsibility
    http://winteryknight.com/2014/.....cal-minds/

    You see, we each have a unique perspective of being outside of time. Simply put, we each seem to be standing on our own little ‘island of now’ as the river of time continually flows past eack of us.

    ‘The experience of ‘the now” also happens to be exactly where Albert Einstein got into trouble with leading philosophers of his day and also happens to be exactly where Einstein eventually got into trouble with quantum mechanics itself. Around 1935, Einstein was asked by Rudolf Carnap (who was a philosopher):

    “Can physics demonstrate the existence of ‘the now’ in order to make the notion of ‘now’ into a scientifically valid term?”
    Rudolf Carnap – Philosopher

    Einstein’s answer was categorical, he said:

    “The experience of ‘the now’ cannot be turned into an object of physical measurement, it can never be a part of physics.”
    – Einstein

    That quote was taken from the last few minutes of this following video.

    Stanley L. Jaki: “The Mind and Its Now”
    https://vimeo.com/10588094

    And here is an article that goes into a bit more detail of that specific encounter between Einstein and Rudolf Carnap:

    The Mind and Its Now – May 22, 2008 – By Stanley L. Jaki
    Excerpt: ,,, Rudolf Carnap, and the only one among them who was bothered with the mind’s experience of its now. His concern for this is noteworthy because he went about it in the wrong way. He thought that physics was the only sound way to know and to know anything. It was therefore only logical on his part that he should approach, we are around 1935, Albert Einstein, the greatest physicist of the day, with the question whether it was possible to turn the experience of the now into a scientific knowledge. Such knowledge must of course be verified with measurement. We do not have the exact record of Carnap’s conversation with Einstein whom he went to visit in Princeton, at eighteen hours by train at that time from Chicago. But from Einstein’s reply which Carnap jotted down later, it is safe to assume that Carnap reasoned with him as outlined above. Einstein’s answer was categorical: The experience of the now cannot be turned into an object of physical measurement. It can never be part of physics.
    http://metanexus.net/essay/mind-and-its-now

    Prior to that encounter with Carnap, Einstein also had another disagreement with another famous philosopher, Henri Bergson, over what the proper definition of time should be (Bergson was also very well versed in the specific mental attribute of the ‘experience of the now’). In fact, that disagreement with Henri Bergson over what the proper definition of time should be was actually one of the primary reasons that Einstein failed to ever receive a Nobel prize for his work on relativity:

    Einstein, Bergson, and the Experiment that Failed: Intellectual Cooperation at the League of Nations! – Jimena Canales
    page 1177
    Excerpt: Bergson temporarily had the last word during their meeting at Société française de philosophie. His intervention negatively affected Einstein’s Nobel Prize, which was given “for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect” and not for relativity. The reasons behind this decision, as stated in the prize’s presentation speech, were related to Bergson’s intervention: “Most discussion [of Einstein’s work] centers on his Theory of Relativity. This pertains to epistemology and has therefore been the subject of lively debate in philosophical circles. It will be no secret that the famous philosopher Bergson in Paris has challenged this theory, while other philosophers have acclaimed it wholeheartedly.”51 For a moment, their debate dragged matters of time out of the solid terrain of “matters of fact” and into the shaky ground of “matters of concern.”52
    https://dash.harvard.edu/bitstream/handle/1/3210598/canales-Einstein,%20Bergson%20and%20the%20Experiment%20that%20Failed%282%29.pdf?sequence=2

    Here is an article that goes into a bit more detail about the particular confrontation between Einstein and Henri Bergson over the proper definition of time:

    Einstein vs Bergson, science vs philosophy and the meaning of time – Wednesday 24 June 2015
    Excerpt: ‘Einstein had been invited by philosophers to speak at their society, and you had this physicist say very clearly that their time did not exist.’
    Bergson was outraged, but the philosopher did not take it lying down. A few months later Einstein was awarded the Nobel Prize for the discovery of the law of photoelectric effect, an area of science that Canales noted, ‘hardly jolted the public’s imagination’. In truth, Einstein coveted recognition for his work on relativity.
    http://www.abc.net.au/radionat.....me/6539568

    The specific statement that Einstein made to Carnap on the train, “The experience of ‘the now’ cannot be turned into an object of physical measurement, it can never be a part of physics.” was a very interesting statement for Einstein to make to the philosopher since “The experience of ‘the now’ has, from many recent experiments in quantum mechanics, established itself as very much being a defining part of our physical measurements in quantum mechanics.

    For instance, the following delayed choice experiment with atoms demonstrated that, “It proves that measurement is everything. At the quantum level, reality does not exist if you are not looking at it,”

    Reality doesn’t exist until we measure it, (Delayed Choice) quantum experiment confirms – Mind = blown. – FIONA MACDONALD – 1 JUN 2015
    Excerpt: “It proves that measurement is everything. At the quantum level, reality does not exist if you are not looking at it,” lead researcher and physicist Andrew Truscott said in a press release.
    http://www.sciencealert.com/re.....t-confirms

  10. 10
    bornagain77 says:

    Likewise, the following violation of Leggett’s inequality stressed the quantum-mechanical assertion that reality does not exist when we’re not observing it.

    Quantum physics says goodbye to reality – Apr 20, 2007
    Excerpt: They found that, just as in the realizations of Bell’s thought experiment, Leggett’s inequality is violated – thus stressing the quantum-mechanical assertion that reality does not exist when we’re not observing it. “Our study shows that ‘just’ giving up the concept of locality would not be enough to obtain a more complete description of quantum mechanics,” Aspelmeyer told Physics Web. “You would also have to give up certain intuitive features of realism.”
    http://physicsworld.com/cws/article/news/27640

    The Mind First and/or Theistic implications of quantum experiments such as the preceding are fairly obvious. As Professor Scott Aaronson of MIT once quipped, “Look, we all have fun ridiculing the creationists,,, But if we accept the usual picture of quantum mechanics, then in a certain sense the situation is far worse: the world (as you experience it) might as well not have existed 10^-43 seconds ago!”

    “Look, we all have fun ridiculing the creationists who think the world sprang into existence on October 23, 4004 BC at 9AM (presumably Babylonian time), with the fossils already in the ground, light from distant stars heading toward us, etc. But if we accept the usual picture of quantum mechanics, then in a certain sense the situation is far worse: the world (as you experience it) might as well not have existed 10^-43 seconds ago!”
    – Scott Aaronson – MIT associate Professor quantum computation – Lecture 11: Decoherence and Hidden Variables

    Besides such experiments as this from quantum mechanics demonstrating that ‘the experience of the now’ is very much a part of present day quantum physics, there is also what is known as the ‘Quantum Zeno Effect’ in quantum mechanics which also clearly demonstrates that ‘the experience of the now’ is very much a part of present day quantum physics.

    An old 2018 entry in wikipedia described the Quantum Zeno effect as such “an unstable particle, if observed continuously, will never decay.”

    Perspectives on the quantum Zeno paradox – 2018
    The quantum Zeno effect is,, an unstable particle, if observed continuously, will never decay.
    https://iopscience.iop.org/article/10.1088/1742-6596/196/1/012018/pdf

    Likewise, the present day entry on wikipedia about the Quantum Zeno effect also provocatively states that “a system can’t change while you are watching it”

    Quantum Zeno effect
    Excerpt: Sometimes this effect is interpreted as “a system can’t change while you are watching it”
    https://en.wikipedia.org/wiki/Quantum_Zeno_effect

    Atheistic materialists have tried to get around the Quantum Zeno effect by postulating that interactions with the environment are sufficient to explain the Quantum Zeno effect.

    Perspectives on the quantum Zeno paradox – 2018
    Excerpt: The references to observations and to wavefunction collapse tend to raise unnecessary questions related to the interpretation of quantum mechanics. Actually, all that is required is that some interaction with an external system disturb the unitary evolution of the quantum system in a way that is effectively like a projection operator.
    https://iopscience.iop.org/article/10.1088/1742-6596/196/1/012018/pdf

    Yet, the following interaction-free measurement of the Quantum Zeno effect demonstrated that the presence of the Quantum Zeno effect can be detected without interacting with a single atom.

    Interaction-free measurements by quantum Zeno stabilization of ultracold atoms – 14 April 2015
    Excerpt: In our experiments, we employ an ultracold gas in an unstable spin configuration, which can undergo a rapid decay. The object—realized by a laser beam—prevents this decay because of the indirect quantum Zeno effect and thus, its presence can be detected without interacting with a single atom.
    http://www.nature.com/ncomms/2.....S-20150415

    In short, the quantum zeno effect, regardless of how atheistic materialists may personally feel about it, is experimentally shown to be a real effect that is not reducible to any materialistic explanation. And thus the original wikipedia statement of, “an unstable particle, if observed continuously, will never decay”, stands as being a true statement.

    Moreover, on top of the quantum zeno effect, in quantum information theory we find that entropy is “a property of an observer who describes a system.”

    As the following 2017 article states: James Clerk Maxwell (said), “The idea of dissipation of energy depends on the extent of our knowledge.”,,,
    quantum information theory,,, describes the spread of information through quantum systems.,,,
    Fifteen years ago, “we thought of entropy as a property of a thermodynamic system,” he said. “Now in (quantum) information theory, we wouldn’t say entropy is a property of a system, but a property of an observer who describes a system.”,,,

    The Quantum Thermodynamics Revolution – May 2017
    Excerpt: the 19th-century physicist James Clerk Maxwell put it, “The idea of dissipation of energy depends on the extent of our knowledge.”
    In recent years, a revolutionary understanding of thermodynamics has emerged that explains this subjectivity using quantum information theory — “a toddler among physical theories,” as del Rio and co-authors put it, that describes the spread of information through quantum systems. Just as thermodynamics initially grew out of trying to improve steam engines, today’s thermodynamicists are mulling over the workings of quantum machines. Shrinking technology — a single-ion engine and three-atom fridge were both experimentally realized for the first time within the past year — is forcing them to extend thermodynamics to the quantum realm, where notions like temperature and work lose their usual meanings, and the classical laws don’t necessarily apply.
    They’ve found new, quantum versions of the laws that scale up to the originals. Rewriting the theory from the bottom up has led experts to recast its basic concepts in terms of its subjective nature, and to unravel the deep and often surprising relationship between energy and information — the abstract 1s and 0s by which physical states are distinguished and knowledge is measured.,,,
    Renato Renner, a professor at ETH Zurich in Switzerland, described this as a radical shift in perspective. Fifteen years ago, “we thought of entropy as a property of a thermodynamic system,” he said. “Now in (quantum) information theory, we wouldn’t say entropy is a property of a system, but a property of an observer who describes a system.”,,,
    https://www.quantamagazine.org/quantum-thermodynamics-revolution/

    The reason why I am very impressed with the preceding experiments demonstrating that the mental attribute of ‘the experience of the now’ is very much a part of entropy, is that the second law of thermodynamics, entropy, is very foundational to any definition of time that we may have.

    In fact, if we saw a video of a broken tea cup putting itself together we would swear that the video was running backwards, i.e. that time was going backwards.

    On top of the fact that entropy is very foundational to any definition of time that we may have, entropy is also, by a very wide margin, the most finely tuned of the initial conditions of the Big Bang. Finely tuned to an almost incomprehensible degree of precision, 1 part in 10 to the 10 to the 123rd power. As Roger Penrose himself stated that, “This now tells us how precise the Creator’s aim must have been: namely to an accuracy of one part in 10^10^123.”

    “This now tells us how precise the Creator’s aim must have been: namely to an accuracy of one part in 10^10^123.”
    Roger Penrose – How special was the big bang? – (from the Emperor’s New Mind, Penrose, pp 339-345 – 1989)

    And yet to repeat, according to quantum information theory, “we wouldn’t say entropy is a property of a system, but a property of an observer who describes a system.”

    This statement is just fascinating! Why in blue blazes should the finely tuned entropic actions of the universe, entropic actions which also happen to explain time itself, even care if I am consciously observing them, and/or describing them, unless ‘the experience of ‘the now’ really is more foundational to reality than the finely tuned 1 in 10^10^123 entropy of the universe is? To state the obvious, this finding of entropy being “a property of an observer who describes a system.” is very friendly to a Mind First, and/or to a Theistic view of reality.

    For instance Romans chapter 8: verses 20 and 21 itself states, “For the creation was subjected to frustration, not by its own choice, but by the will of the one who subjected it, in hope that the creation itself will be liberated from its bondage to decay and brought into the glorious freedom of the children of God.”

    Romans 8:20-21
    For the creation was subjected to frustration, not by its own choice, but by the will of the one who subjected it, in hope that the creation itself will be liberated from its bondage to decay and brought into the glorious freedom of the children of God.

    Thus, contrary to what Einstein himself thought was possible for experimental physics, receent advances in quantum mechanics, particularly advances in quantum information theory, have now shown, in overwhelming fashion, that ‘the experience of the now’ is very much a part of experimental physics. In fact, due to advances in quantum mechanics, it would now be much more appropriate to rephrase Einstein’s answer to the philosopher Rudolph Carnap in this way:

    “It is impossible for “the experience of ‘the now’” to ever be divorced from physical measurement, it will always be a part of physics.”

    To repeat what was said in the delayed choice experiment with atoms, “It proves that measurement is everything. At the quantum level, reality does not exist if you are not looking at it,”

    Reality doesn’t exist until we measure it, (Delayed Choice) quantum experiment confirms – Mind = blown. – FIONA MACDONALD – 1 JUN 2015
    Excerpt: “It proves that measurement is everything. At the quantum level, reality does not exist if you are not looking at it,” lead researcher and physicist Andrew Truscott said in a press release.
    http://www.sciencealert.com/re.....t-confirms

    Moreover, although Einstein was shown to be wrong, via quantum mechanics, in his confrontation with philosophers over the proper definition of time, i.e. over ‘the experience of the now’, never-the-less Einstein’s special theory of relativity is also very friendly to a Theistic view of reality.

    We now know from special relativity, time, as we understand it, comes to a complete stop for a hypothetical observer travelling at the speed of light.

    To grasp the whole concept of time coming to a complete stop at the speed of light a little more easily, imagine moving away from the face of a clock at the speed of light. Would not the hands on the clock stay stationary as you moved away from the face of the clock at the speed of light? Moving away from the face of a clock at the speed of light happens to be the very same ‘thought experiment’ that gave Einstein his breakthrough insight into special relativity. Here is a short clip from a video that gives us a look into Einstein’s breakthrough insight.

    Einstein: Einstein’s Miracle Year (‘Insight into Eternity’ – Thought Experiment 55 second mark) – video
    http://www.history.com/topics/.....racle-year

    That time, as we understand it, comes to a complete stop at the speed of light, and yet light moves from point A to point B in our universe, and thus light is obviously not ‘frozen within time, has some fairly profound implications.

    “The laws of relativity have changed timeless existence from a theological claim to a physical reality. Light, you see, is outside of time, a fact of nature proven in thousands of experiments at hundreds of universities. I don’t pretend to know how tomorrow can exist simultaneously with today and yesterday. But at the speed of light they actually and rigorously do. Time does not pass.”
    Dr. Richard Swenson – More Than Meets The Eye, Chpt. 11

    The only way it is possible for time not to pass for light, and yet for light to move from point A to point B in our universe, is if light is of a higher dimensional value of time than the temporal time we are currently living in. Otherwise light would simply be ‘frozen within time’ to our temporal frame of reference.

    And indeed that is exactly what we find. “Hermann Minkowski- one of the math professors of a young Einstein in Zurich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space.”

    Spacetime
    Excerpt: In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zurich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the definition of a spacetime interval that combines distance and time. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded.
    Minkowski’s geometric interpretation of relativity was to prove vital to Einstein’s development of his 1915 general theory of relativity, wherein he showed that spacetime becomes curved in the presence of mass or energy.,,,
    Einstein, for his part, was initially dismissive of Minkowski’s geometric interpretation of special relativity, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital, and in 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity.[10]:151–152 Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as Minkowski spacetime.
    https://en.wikipedia.org/wiki/Spacetime

  11. 11
    bornagain77 says:

    One way for us to more easily understand this higher dimensional framework for time that light exist in is to visualize what would happen if a hypothetical observer approached the speed of light.
    In the following video clip, which was made by two Australian University Physics Professors, we find that the 3-Dimensional world ‘folds and collapses’ into a tunnel shape as a ‘hypothetical’ observer approaches the ‘higher dimension’ of the speed of light.

    Optical Effects of Special Relativity – video
    https://www.youtube.com/watch?v=JQnHTKZBTI4

    OK now that we have outlined the basics of what we know to be true from special relativity, It is very interesting to note that many of the characteristics found in heavenly Near Death Experience testimonies are exactly what we would expect to see from what we now know to be true about Special Relativity.

    For instance, many times people who have had a Near Death Experience mention that their perception of time was radically altered. In the following video clip, Mickey Robinson gives his Near Death testimony of what it felt like for him to experience a ‘timeless eternity’.

    ‘In the ‘spirit world,,, instantly, there was no sense of time. See, everything on earth is related to time. You got up this morning, you are going to go to bed tonight. Something is new, it will get old. Something is born, it’s going to die. Everything on the physical plane is relative to time, but everything in the spiritual plane is relative to eternity. Instantly I was in total consciousness and awareness of eternity, and you and I as we live in this earth cannot even comprehend it, because everything that we have here is filled within the veil of the temporal life. In the spirit life that is more real than anything else and it is awesome. Eternity as a concept is awesome. There is no such thing as time. I knew that whatever happened was going to go on and on.’
    In The Presence Of Almighty God – The NDE of Mickey Robinson – video (testimony starts at 27:45 minute mark)
    https://www.youtube.com/watch?v=voak1RM-pXo

    And here are a few more quotes from people who have experienced Near Death, that speak of how their perception of time was radically altered as they were outside of their material body during their NDEs.

    ‘Earthly time has no meaning in the spirit realm. There is no concept of before or after. Everything – past, present, future – exists simultaneously.’
    – Kimberly Clark Sharp – Near Death Experiencer

    ‘There is no way to tell whether minutes, hours or years go by. Existence is the only reality and it is inseparable from the eternal now.’
    – John Star – NDE Experiencer

    As well, Near Death Experiencers also frequently mention going through a tunnel to a higher heavenly dimension:

    Ask the Experts: What Is a Near-Death Experience (NDE)? – article with video
    Excerpt: “Very often as they’re moving through the tunnel, there’s a very bright mystical light … not like a light we’re used to in our earthly lives. People call this mystical light, brilliant like a million times a million suns…”
    – Jeffrey Long M.D. – has studied NDE’s extensively

    The Tunnel and the Near-Death Experience
    Excerpt: One of the nine elements that generally occur during NDEs is the tunnel experience. This involves being drawn into darkness through a tunnel, at an extremely high speed, until reaching a realm of radiant golden-white light.

    In the following video, Barbara Springer gives her testimony as to what it felt like for her to go through the tunnel:

    “I started to move toward the light. The way I moved, the physics, was completely different than it is here on Earth. It was something I had never felt before and never felt since. It was a whole different sensation of motion. I obviously wasn’t walking or skipping or crawling. I was not floating. I was flowing. I was flowing toward the light. I was accelerating and I knew I was accelerating, but then again, I didn’t really feel the acceleration. I just knew I was accelerating toward the light. Again, the physics was different – the physics of motion of time, space, travel. It was completely different in that tunnel, than it is here on Earth. I came out into the light and when I came out into the light, I realized that I was in heaven.”
    Barbara Springer – Near Death Experience – The Tunnel – video
    https://www.youtube.com/watch?v=gv2jLeoAcMI

    And in the following audio clip, Vicki Noratuk, (who has been blind from birth, besides being able to ‘miraculously” see for the first time during in her life during her Near Death Experience), Vicki also gives testimony of going through a tunnel:

    “I was in a body, and the only way that I can describe it was a body of energy, or of light. And this body had a form. It had a head, it had arms and it had legs. And it was like it was made out of light. And it was everything that was me. All of my memories, my consciousness, everything.”,,, “And then this vehicle formed itself around me. Vehicle is the only thing, or tube, or something, but it was a mode of transportation that’s for sure! And it formed around me. And there was no one in it with me. I was in it alone. But I knew there were other people ahead of me and behind me. What they were doing I don’t know, but there were people ahead of me and people behind me, but I was alone in my particular conveyance. And I could see out of it. And it went at a tremendously, horrifically, rapid rate of speed. But it wasn’t unpleasant. It was beautiful in fact.,, I was reclining in this thing, I wasn’t sitting straight up, but I wasn’t lying down either. I was sitting back. And it was just so fast. I can’t even begin to tell you where it went or whatever it was just fast!” –
    Vicki’s NDE – Blind since birth –
    https://www.youtube.com/watch?v=e65KhcCS5-Y

    And in the following quotes, the two Near Death Experiencers both testify that they firmly believed that they were in a higher heavenly dimension that is above this three-dimensional world, and that the reason that they have a very difficult time explaining what their Near Death Experiences actually felt like is because we simply don’t currently have the words to properly describe that higher dimension:

    “Regardless, it is impossible for me to adequately describe what I saw and felt. When I try to recount my experiences now, the description feels very pale. I feel as though I’m trying to describe a three-dimensional experience while living in a two-dimensional world. The appropriate words, descriptions and concepts don’t even exist in our current language. I have subsequently read the accounts of other people’s near-death experiences and their portrayals of heaven and I able to see the same limitations in their descriptions and vocabulary that I see in my own.”
    Mary C. Neal, MD – To Heaven And Back pg. 71

    “Well, when I was taking geometry, they always told me there were only three dimensions, and I always just accepted that. But they were wrong. There are more… And that is why so hard for me to tell you this. I have to describe with words that are three-dimensional. That’s as close as I can get to it, but it’s really not adequate.”
    John Burke – Imagine Heaven pg. 51 – quoting a Near Death Experiencer

    That what we now know to be true from special relativity, (namely that it outlines a ‘timeless’, i.e. eternal, dimesion that exists above this temporal dimension), would fit hand and glove with the personal testimonies of people who have had a deep heavenly NDE is, needless to say, powerful evidence that their testimonies are, in fact, true and that they are accurately describing the ‘reality’ of a higher heavenly dimension that exists above this temporal dimension.

    And while it is certainly true that one cannot place too much emphasis on just one Near Death Experience as being undeniably true, none the less, since these Near Death experiences are verified repeatedly by millions of different people who have died for a short while and have come back to tell us of their experiences, then the ‘subjective observations’ of these people, (of a timeless eternity and of ‘going through a tunnel’ to a higher dimension), are, none the less, extremely reliable in that they do indeed exactly match the characteristics of what we would expect to be true beforehand from what we now know to be true, scientifically, from special relativity.

    I would even go so far as to say that such corroboration from ‘non-physicists’, who know nothing about the intricacies of special relativity, is a complete scientific verification of the overall validity of their personal NDE testimonies.

    Luke 23:43
    Jesus answered him, “Truly I tell you, today you will be with me in paradise.”

    2 Corinthians 12:2-4
    I know a man in Christ who fourteen years ago was caught up to the third heaven. Whether it was in the body or out of the body I do not know—God knows. And I know that this man—whether in the body or apart from the body I do not know, but God knows— was caught up to paradise and heard inexpressible things, things that no one is permitted to tell.

    Supplemental quote: ‘How You Think About Heaven Affects Everything in Life,’

    Texas Pastor John Burke Says Near-Death Experiences Are ‘Amazingly Biblical’ (Video) – Oct 25, 2015
    ‘How You Think About Heaven Affects Everything in Life,’ Says Gateway Church Pastor
    http://www.christianpost.com/n.....eo-148156/

    Supplemental note: The reality of a soul that is capable of living beyond the death of our material bodies is now strongly supported by advances in quantum biology:

    Darwinian Materialism vs. Quantum Biology – Part II – video
    https://www.youtube.com/watch?v=oSig2CsjKbg

    Verses:

    Mark 8:37
    Is anything worth more than your soul?

    Matthew 6:33
    But seek first the kingdom of God and his righteousness, and all these things will be added to you.

    Footnote. The bulk of refrences in this post were taken from these two videos:

    How Quantum Mechanics and Consciousness Correlate – video
    https://www.youtube.com/watch?v=4f0hL3Nrdas

    Quantum Mechanics, Special Relativity, General Relativity and Christianity – video
    https://www.youtube.com/watch?v=h4QDy1Soolo

  12. 12
    Granville Sewell says:

    Asauber (1): I agree, infinity is a useful mathematical concept, but I don’t believe there can be an infinite amount of anything: space, time, matter, energy… (Disclaimer: I could be wrong!) And I agree that an infinite past is even more problematic than an infinite future. Of course a finite past or finite future is pretty hard to fathom too!

    Here’s an only slightly related puzzle for your entertainment. Are “most” positive integers prime? You will probably say, most are not prime (composite) because primes are more and more rare as you count upwards: 2,3,4,5,6,7,… However, what if I list the integers in the following order–first 2 primes, first composite, next 2 primes, next composite, next 2 primes…:

    2,3,4, 5,7,6, 11,13,8, 17,19,9…

    this is a complete list of all positive integers, that is, any given integer is eventually in the list, so why is my list not as good as yours? And in my list, 2/3 of the integers are prime.

    The issue is, there are an infinite number of primes and and infinite number of nonprimes, so who’s to
    say which countably infinite list is bigger? On the other hand, I think it is correct to say “most” real
    numbers are irrational, because there are a countably infinite (you can list them in such a way as to
    get to any rational number eventually) number of rational numbers, but an uncountably large number of irrationals (there is no algorithm for listing them such that you eventually include every irrational number).

    Moral: infinity is a strange number.

  13. 13
    JVL says:

    ET:

    Oh dear, a discussion of infinity. Are you going to participate?

  14. 14
    ET says:

    Oh dear. I am sure that JVL still doesn’t understand that infinity is a journey…

  15. 15
    JVL says:

    ET, 14: Oh dear. I am sure that JVL still doesn’t understand that infinity is a journey…

    Why don’t you ask Dr Sewell? See what he says. Ask him if the infinity of the evens is half the infinity of the whole numbers. Go on.

  16. 16
    ET says:

    What’s the relevance to the topic? Why don’t YOU ask if anyone uses the concept that the set of evens = the set of whole numbers for anything? Does saying that have any utility? And if the world accepted that the set of evens was half that of the set of whole numbers would anything beyond textbooks and teaching be affected? Go on.

  17. 17
    JVL says:

    ET, 16;,

    I’m happy to ask:

    Dr Sewell I’m wondering if you think there is any use for the concept that the cardinality of the positive even integers is the same as the cardinality of the positive integers? ET says it’s not true (on his own blog) and that it’s useless. What do you think?

  18. 18
    ET says:

    Read his comment in 12, JVL.

    The issue is, there are an infinite number of primes and infinite number of nonprimes, so who’s to say which countably infinite list is bigger?

    And yes, I do say it doesn’t have any utility at all to say that all countably infinite sets have the same cardinality. No one uses that concept for any practical application.

  19. 19
    JVL says:

    ET, 18:

    I’ve asked, let’s see if he answers.

  20. 20
    ET says:

    I understand your reading comprehension issues. Why don’t you go to some engineering group and ask them. Or chemists, physicists or mathematicians. Bring them here.

  21. 21
    JVL says:

    ET, 20:

    I’ve asked let’s see if Dr Sewell respond.

    I’m happy to go ask some engineers and physicists and chemists and particularly mathematicians. If you specify a forum which we can both access then I’d be glad to try that. I don’t think it’s fair to ask them to come to an ID forum as that has nothing to do with the question.

  22. 22
    ET says:

    Go ask. If you find something I have no doubt that you will come running back. I also find it very telling that every time that YOU try to answer the question you refer to something that has nothing to do with the question. The question has nothing to do with whether or not set theory is of any use. The question has nothing to do with whether or not the concept of infinity is of any use. Yet you always bring those up as if that is some kind of argument against what I am saying.

    But here are questions for you:

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

  23. 23
    JVL says:

    ET, 22:

    The cardinality/size of sets has nothing to do with the time it takes to count them. The set of positive even integers has the same cardinality os the set of positive integers. This is well established and accepted mathematics. You may not know or accept that this is foundational to modern mathematics but it is.

  24. 24
    kairosfocus says:

    JVL,

    nope. It is a fact that time lapses in a way that we see finite duration, causally successive, cumulative stages. One year succeeds and builds on another. Taking in a past that might extend beyond the singularity, we can simply count stages.

    In such a case, the count is stage-wise.

    Now, say let the bang be 0, we count up to now, and let us project beyond the bang. Now, a pause, we can use a more relevant span than N or Z in R, going to hyperreals R*, where some H is such that 1/H is h, smaller than any n we may successively count to. The h is of course an infinitesimal.

    Now, let – H be a hyperinteger in Z* so that we can address what an infinite past means and why it is infeasible; we are summarising an earlier discussion. We can see

    . . . -H, -H+1, -H+2 . . . -H+k, -H+k+1, . . . -p, -p+1, . . . -2, -1, 0, 1, 2 . . . n, now.

    Were there an actually infinite past, every finitely remote past 0, -p, etc would have a transfinite further past beyond to the left. H allows us to see implications. From such a transfinitely remote H and beyond, we see a count up to some k beyond -H.

    But as we go on, we see that counting beyond -H+k is no different from counting up from -H, i.e. the ellipsis to -p is not span-able in finite stage steps precisely because the mileposts of hyperintegers counted up from -H are inexhaustible. That also obtains for -H+k and so forth. We cannot traverse a transfinite span by means of a finite stage succession of causal-temporal steps in sequence.

    This is different from infinite, converging series where each step takes shorter times converging on 0, as solves Zeno.

    There is a logical, structural, quantitative reason why there cannot be a transfinite actual past.

    Our world and whatever causal-temporal matrix may have spawned it will be finite in the past. To get a root of reality, we need a different order of being, necessary being.

    KF

  25. 25
    kairosfocus says:

    PS: Note, the timers are counting in finite stage steps. At any time t, one will be about half the other, providing t is finitely remote from the start. That is, there is a question that time is potentially infinite going forward but not exhausted. So on the dynamics, at any attained t, that will be the case. The onward succession has no finite bound as N has cardinality aleph null, however, the hyper integers in the family of H will exceed any n in N mileposting R. By finite increments from 0 we cannot span to such an H.

  26. 26
    kairosfocus says:

    PPS: We recognise that we have a quantity aleph null, as the metric of endless counting. It has different properties from finite numbers, and 0,1,2 . . . maps to 0,2,4 . . . so we see they pose the same ordinals and have the same overall quantity. We define the transfinite ordinal w as successor to the span, and go on from there, mapping to hyperreals and surreals.

  27. 27
    ET says:

    JVL:

    The cardinality/size of sets has nothing to do with the time it takes to count them.

    I never said that it did. Answer my questions and stop being such a coward.

  28. 28
    JVL says:

    ET, 27: I never said that it did. Answer my questions and stop being such a coward.

    The set of all positive even integers has the same cardinality as the set of all positive integers. You can look it up in many, many different places. It doesn’t matter about your counting procedure. We’re not considering a count at some time and infinity is not a “time”. Your question has nothing to do with the cardinality of infinite sets.

  29. 29
    ET says:

    Answer my questions and stop being such a coward, JVL. My questions have everything to do with the cardinality of infinite sets. And your responses prove that you do not understand that infinity is a journey.

    Cardinality has to work for ALL sets. My example pertains to two specific sets.

    IF the set of all positive even integers has the same cardinality as the set of all positive integers, THEN set subtraction would not be able to prove otherwise. And yet it does.

  30. 30
    ET says:

    Jerad won’t answer my questions because if he did then he would show that my premise is correct. And I am more than OK with that.

    Thanks, Jerad.

  31. 31
    JVL says:

    ET, 29: My questions have everything to do with the cardinality of infinite sets. And your responses prove that you do not understand that infinity is a journey.

    You don’t understand set theory.

    Cardinality has to work for ALL sets. My example pertains to two specific sets.

    The accepted version does work for all sets. You can’t even figure out the cardinality of some sets. Like the primes; what’s the cardinality of the primes?

    IF the set of all positive even integers has the same cardinality as the set of all positive integers, THEN set subtraction would not be able to prove otherwise. And yet it does.

    Nope, it doesn’t. If you take the set of the positive integers and “subtract” the set of positive even integers you get the set of positive odd integers and all three of those sets have the same cardinality. It’s easy.

    Jerad won’t answer my questions because if he did then he would show that my premise is correct. And I am more than OK with that.

    You don’t understand set theory. If you count in the manner you describe and you stop at some time then one counter would be twice as big as the other. But that wouldn’t be at infinity would it? You’re questions have nothing to do with how set theory works.

    Look it up. It’s easy to find out the way it works.

  32. 32
    ET says:

    Here we go. Pound sand, Jerad. Thank you for proving that you are a coward. All you can do is hurl dales accusations. That makes you a punk, too.

    Sets are COLLECTIONS of things. My examples are of things being collected. My example has one counter always and forever having more than the other. At EVERY finite point in time, into infinity.

    You can’t even read for comprehension.

    IF the set of all positive even integers has the same cardinality as the set of all positive integers, THEN set subtraction would not be able to prove otherwise. And yet it does.

    That is a FACT.

  33. 33
    ET says:

    And we are right back to the fact that saying two countably infinite sets having the same cardinality is of no use. That means it is meaningless to say such a thing. It also means one has to lie when set subtraction proves that one countably infinite set has more elements than another.

  34. 34
    ET says:

    hurl FALSE accusations-

    Bring back the edit feature… Please

  35. 35
    JVL says:

    ET, 32: Here we go. Pound sand, Jerad. Thank you for proving that you are a coward. All you can do is hurl dales accusations. That makes you a punk, too.

    It’s true, you don’t understand set theory. I mean real set theory beyond Algebra 101.

    Sets are COLLECTIONS of things. My examples are of things being collected. My example has one counter always and forever having more than the other. At EVERY finite point in time, into infinity.

    Things are different for infinity. Look it up.

    You can’t even read for comprehension.

    Whatever. You don’t understand set theory.

    IF the set of all positive even integers has the same cardinality as the set of all positive integers, THEN set subtraction would not be able to prove otherwise. And yet it does.

    Nope, it doesn’t. The set of all positive integers, the set of all positive even integers, the set of all positive odd integers, the set of all positive multiples of three, the set of all positive prime numbers, the set of all positive powers of 4 all have the same cardinality. The set of all real numbers has a different cardinality. Look it up.

    That is a FACT.

    Nope. Look it up. It doesn’t matter what you think, what matters is what is true. Look it up.

    And we are right back to the fact that saying two countably infinite sets having the same cardinality is of no use. That means it is meaningless to say such a thing. It also means one has to lie when set subtraction proves that one countably infinite set has more elements than another.

    I’m sorry the math escapes you. You’re not the only one if that makes you feel better.

  36. 36
    JVL says:

    <b<ET: Bring back the edit feature… Please

    Something we can definitely agree on!! Who thought taking it away was a good idea?

  37. 37
    ET says:

    Jerad, you are a liar. That you have to use false accusations, seals the deal. Reality escapes you. The ability to think for yourself, escapes you. Only a moron thinks that something special happens with infinity. And here you are. Infinity is just more of the same.

    IF the set of all positive even integers has the same cardinality as the set of all positive integers, THEN set subtraction would not be able to prove otherwise. And yet it does.

    Take the set of all positive integers and subtract the set of all evens. If the two sets had the same cardinality the answer would be 0. And yet the answer is the set of all odd integers.

    And we are right back to the fact that saying two countably infinite sets having the same cardinality is of no use. That means it is meaningless to say such a thing. It also means one has to lie when set subtraction proves that one countably infinite set has more elements than another.

    And all Jerad can do is whine like a little baby.

    “Things are different for infinity” comes from the little minds that cannot grasp the concept.

  38. 38
    JVL says:

    ET: 37: Jerad, you are a liar. That you have to use false accusations, seals the deal. Reality escapes you. The ability to think for yourself, escapes you. Only a moron thinks that something special happens with infinity. And here you are. Infinity is just more of the same.

    Nope, infinity is not just more of the same. You don’t have to believe me, look it up! Are you afraid to find out I’m right?

    IF the set of all positive even integers has the same cardinality as the set of all positive integers, THEN set subtraction would not be able to prove otherwise. And yet it does.

    Nope, that’s not right. Look it up if you don’t believe me.

    Take the set of all positive integers and subtract the set of all evens. If the two sets had the same cardinality the answer would be 0. And yet the answer is the set of all odd integers.

    Yup, and all three sets have the same cardinality. Look it up. It’s easy to look up.

    And we are right back to the fact that saying two countably infinite sets having the same cardinality is of no use. That means it is meaningless to say such a thing. It also means one has to lie when set subtraction proves that one countably infinite set has more elements than another.

    Look it up. You’ll never believe me so look it up.

    And all Jerad can do is whine like a little baby.

    Being right is not whining.

    “Things are different for infinity” comes from the little minds that cannot grasp the concept.

    I’m not the one that doesn’t understand how set theory works.

    All you have to do is look up the pertinent mathematics to see I’m correct. It’s easy.

  39. 39
    ET says:

    JVL:

    Nope, infinity is not just more of the same.

    Of course it is. That is what the … means- more of the same. Are you really that daft? Look it up, Jerad. Or shut up.

    IF the set of all positive even integers has the same cardinality as the set of all positive integers, THEN set subtraction would not be able to prove otherwise. And yet it does.

    Jerad can whine all he wants but what I said is a fact.

    Take the set of all positive integers and subtract the set of all evens. If the two sets had the same cardinality the answer would be 0. And yet the answer is the set of all odd integers.

    Cardinality refers to the number of elements in a set. Therefore if set subtraction comes back with something other than nothing the cardinalities cannot be the same. math 101.

    And we are right back to the fact that saying two countably infinite sets having the same cardinality is of no use. That means it is meaningless to say such a thing. It also means one has to lie when set subtraction proves that one countably infinite set has more elements than another.

    I looked it up and no one uses that concept for anything. All Jerad can do is lie and whine.

    I’m not the one that doesn’t understand how set theory works.

    I understand how set theory works, Jerad. Clearly you cannot think for yourself.

    “Things are different for infinity” comes from the little minds that cannot grasp the concept.

    Still stands.

  40. 40
    ET says:

    And we are right back to the fact that saying two countably infinite sets having the same cardinality is of no use. That means it is meaningless to say such a thing. It also means one has to lie when set subtraction proves that one countably infinite set has more elements than another.

    The concept that all countably infinite sets have the same cardinality is useless. Meaning it doesn’t have any practical value. No one uses it for anything. And Jerad has NEVER found anything that says otherwise.

  41. 41
    JVL says:

    ET, 39: Of course it is. That is what the … means- more of the same. Are you really that daft? Look it up, Jerad. Or shut up.

    I know what infinity means in mathematics. I’ve worked with in in Calculus, Analysis, Set Theory, Complex Analysis, Statistics, etc.

    IF the set of all positive even integers has the same cardinality as the set of all positive integers, THEN set subtraction would not be able to prove otherwise. And yet it does.

    Repeating over and over again doesn’t make it right.

    Jerad can whine all he wants but what I said is a fact.

    Nope. Look it up. OR: find some reference that agrees with you.

    Take the set of all positive integers and subtract the set of all evens. If the two sets had the same cardinality the answer would be 0. And yet the answer is the set of all odd integers.

    Yup, which has the same cardinality of the evens and the integers. And the rational numbers by the way.

    Cardinality refers to the number of elements in a set. Therefore if set subtraction comes back with something other than nothing the cardinalities cannot be the same. math 101.

    Not with infinite sets. Look it up.

    And we are right back to the fact that saying two countably infinite sets having the same cardinality is of no use. That means it is meaningless to say such a thing. It also means one has to lie when set subtraction proves that one countably infinite set has more elements than another.

    You can repeat yourself all you want, what you are saying is still not correct. Look it up.

    I looked it up and no one uses that concept for anything. All Jerad can do is lie and whine.

    I’ll leave it up to anyone else reading this to look it up for themselves and see.

    I understand how set theory works, Jerad. Clearly you cannot think for yourself.

    Being right is okay with me.

    “Things are different for infinity” comes from the little minds that cannot grasp the concept. Still stands.

    Being insulting doesn’t make you right.

    And we are right back to the fact that saying two countably infinite sets having the same cardinality is of no use. That means it is meaningless to say such a thing. It also means one has to lie when set subtraction proves that one countably infinite set has more elements than another.

    Repeating the same thing over and over again doesn’t make it correct.

    The concept that all countably infinite sets have the same cardinality is useless. Meaning it doesn’t have any practical value. No one uses it for anything. And Jerad has NEVER found anything that says otherwise.

    Useful or not it’s still correct, which you can easily verify by looking it up.

  42. 42
    ET says:

    Jerad:

    Being insulting doesn’t make you right

    Ad yet all you do is try to insult me.

    Repeating over and over again doesn’t make it right.

    I repeat because it is right and there isn’t anything you can do or say.

    And if a concept isn’t useful that means it is meaningless. And that means anyone can say anything and nothing changes.

    The concept that all countably infinite sets have the same cardinality is useless. Meaning it doesn’t have any practical value. No one uses it for anything. And Jerad has NEVER found anything that says otherwise.

    Jerad doesn’t understand infinity, and it shows. Jerad doesn’t understand sets, and it shows.

  43. 43
    ET says:

    And we are right back to the fact that saying two countably infinite sets having the same cardinality is of no use. That means it is meaningless to say such a thing. It also means one has to lie when set subtraction proves that one countably infinite set has more elements than another.

    Please, by all means, look it up. I challenge any and every one to find a practical use for saying that all countably infinite sets have the same cardinality.

  44. 44
    JVL says:

    ET, 42: Ad yet all you do is try to insult me.

    It’s just a statement of fact. Your statements clearly indicate you don’t understand how set theory works beyond the basic simple operations.

    I repeat because it is right and there isn’t anything you can do or say.

    I don’t have to do or say anything: what you say is incorrect as can be easily verified.

    And if a concept isn’t useful that means it is meaningless. And that means anyone can say anything and nothing changes.

    Just because you don’t use it or understand the uses doesn’t mean it’s useless or false.

    The concept that all countably infinite sets have the same cardinality is useless. Meaning it doesn’t have any practical value. No one uses it for anything. And Jerad has NEVER found anything that says otherwise.

    Look up Set Theory as in Cantor’s set theory.

    Jerad doesn’t understand infinity, and it shows. Jerad doesn’t understand sets, and it shows.

    A simple online search will show who is correct.

    And we are right back to the fact that saying two countably infinite sets having the same cardinality is of no use. That means it is meaningless to say such a thing. It also means one has to lie when set subtraction proves that one countably infinite set has more elements than another.

    Still incorrect.

    Please, by all means, look it up. I challenge any and every one to find a practical use for saying that all countably infinite sets have the same cardinality.

    It’s useful to mathematicians. And it’s true as well.

  45. 45
    ET says:

    Jeard, your opinions are full of crap. And all you have are your opinions.

    Just because you don’t use it or understand the uses doesn’t mean it’s useless or false.

    No one uses it.

    Look up Set Theory as in Cantor’s set theory.

    I have.

    Still incorrect.

    Your opinion, which stinks.

    It’s useful to mathematicians.

    Liar.

    Set subtraction can prove that one countably infinite set has more elements than another. And all Jerad can do is reference a dead guy who didn’t understand relativity.

  46. 46
    ET says:

    It is very telling that Jerad refuses to answer my questions and respond to my arguments.

  47. 47
    JVL says:

    From: https://en.wikipedia.org/wiki/Set_theory

    Elementary set theory can be studied informally and intuitively, and so can be taught in primary schools using Venn diagrams. The intuitive approach tacitly assumes that a set may be formed from the class of all objects satisfying any particular defining condition. This assumption gives rise to paradoxes, the simplest and best known of which are Russell’s paradox and the Burali-Forti paradox. Axiomatic set theory was originally devised to rid set theory of such paradoxes.[note 1]

    The most widely studied systems of axiomatic set theory imply that all sets form a cumulative hierarchy. Such systems come in two flavors, those whose ontology consists of:

    Sets alone. This includes the most common axiomatic set theory, Zermelo–Fraenkel set theory with the Axiom of Choice (ZFC). Fragments of ZFC include:
    Zermelo set theory, which replaces the axiom schema of replacement with that of separation;
    General set theory, a small fragment of Zermelo set theory sufficient for the Peano axioms and finite sets;
    Kripke–Platek set theory, which omits the axioms of infinity, powerset, and choice, and weakens the axiom schemata of separation and replacement.
    Sets and proper classes. These include Von Neumann–Bernays–Gödel set theory, which has the same strength as ZFC for theorems about sets alone, and Morse–Kelley set theory and Tarski–Grothendieck set theory, both of which are stronger than ZFC.
    The above systems can be modified to allow urelements, objects that can be members of sets but that are not themselves sets and do not have any members.

    The New Foundations systems of NFU (allowing urelements) and NF (lacking them) are not based on a cumulative hierarchy. NF and NFU include a “set of everything, ” relative to which every set has a complement. In these systems urelements matter, because NF, but not NFU, produces sets for which the axiom of choice does not hold.

    Systems of constructive set theory, such as CST, CZF, and IZF, embed their set axioms in intuitionistic instead of classical logic. Yet other systems accept classical logic but feature a nonstandard membership relation. These include rough set theory and fuzzy set theory, in which the value of an atomic formula embodying the membership relation is not simply True or False. The Boolean-valued models of ZFC are a related subject.

    An enrichment of ZFC called internal set theory was proposed by Edward Nelson in 1977.

    That’s the real stuff.

    Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice.[1] Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community. Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals.

    Set theory as a foundation for mathematical analysis, topology, abstract algebra, and discrete mathematics is likewise uncontroversial; mathematicians accept that (in principle) theorems in these areas can be derived from the relevant definitions and the axioms of set theory. Few full derivations of complex mathematical theorems from set theory have been formally verified, however, because such formal derivations are often much longer than the natural language proofs mathematicians commonly present. One verification project, Metamath, includes human-written, computer-verified derivations of more than 12,000 theorems starting from ZFC set theory, first-order logic and propositional logic.

    There’s lots of stuff on countability here: https://en.wikipedia.org/wiki/Countable_set

    Remember that the integers are a countably infinite set.

    The most significant contributions to the field were made by Georg Cantor, a genius of the first order. From his article:

    Cantor’s first set theory article contains Georg Cantor’s first theorems of transfinite set theory, which studies infinite sets and their properties. One of these theorems is his “revolutionary discovery” that the set of all real numbers is uncountably, rather than countably, infinite.[1] This theorem is proved using Cantor’s first uncountability proof, which differs from the more familiar proof using his diagonal argument. The title of the article, “On a Property of the Collection of All Real Algebraic Numbers” (“Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen”), refers to its first theorem: the set of real algebraic numbers is countable. Cantor’s article was published in 1874. In 1879, he modified his uncountability proof by using the topological notion of a set being dense in an interval.

    Cantor’s article also contains a proof of the existence of transcendental numbers. As early as 1930, mathematicians have disagreed on whether this proof is constructive or non-constructive. Books as recent as 2014 and 2015 indicate that this disagreement has not been resolved. Since Cantor’s proof either constructs transcendental numbers or does not, an analysis of his article can determine whether his proof is constructive or non-constructive. Cantor’s correspondence with Richard Dedekind shows the development of his ideas and reveals that he had a choice between two proofs, one that uses the uncountability of the real numbers and one that does not.

    Historians of mathematics have examined Cantor’s article and the circumstances in which it was written. For example, they have discovered that Cantor was advised to leave out his uncountability theorem in the article he submitted?—?he added it during proofreading. They have traced this and other facts about the article to the influence of Karl Weierstrass and Leopold Kronecker. Historians have also studied Dedekind’s contributions to the article, including his contributions to the theorem on the countability of the real algebraic numbers. In addition, they have recognized the role played by the uncountability theorem and the concept of countability in the development of set theory, measure theory, and the Lebesgue integral.

    The distinction between countable and uncountable sets is key and a very, very obvious side note in the whole discussion is the fact that the positive integers and the positive even integers have the same cardinality. That fact is all part of a class of work that many mathematicians feel is fundamental to modern mathematics or at least some parts. That’s why it’s useful; it unpins a lot of other work.

  48. 48
    JVL says:

    ET, 45: Jeard, your opinions are full of crap. And all you have are your opinions.

    They’re not my opinions. What I am saying is correct.

    No one uses it.

    Mathematicians use it. And, by transference, many, many other sciences.

    Your opinion, which stinks.

    Not an opinion. What I am saying is correct.

    Set subtraction can prove that one countably infinite set has more elements than another. And all Jerad can do is reference a dead guy who didn’t understand relativity.

    All countably infinite sets have the same cardinality. Cantor proved it. I can explain the reasoning if anyone wants me to. Or you can look it up, the truth of my statements remains.

    It is very telling that Jerad refuses to answer my questions and respond to my arguments.

    Your arguments are incorrect, infinite sets do not work they way you think they do. I have established that Cantor’s set theory is considered fundamental to modern mathematics by many mathematicians for different parts of mathematics at least. It’s like the foundation of a building which surely is very useful. Everything I say can be verified by doing a bit of work and searching online.

  49. 49
    JVL says:

    Correction in 47 above, last line:

    “unpins” should be “underpins” but “supports” would have been a better descriptive actually.

  50. 50
    JVL says:

    Just in case someone wants an actual proof that the cardinality of the positive even integers is the same as the positive integers you can find it here along with some other proofs.

    https://courses.cs.cornell.edu/cs2800/wiki/index.php/FA18:Lecture_8_cardinality

  51. 51
    ET says:

    They are your opinions. Set subtraction proves that what you are saying is nonsense. So you ignore it.

    No one uses the concept under discussion. No one.

    Cantor didn’t prove anything. My arguments are spot on. My example proves that Jerad cannot think.

    And as predicted Jerad retreats to “set theory”. You are a coward, Jerad. And a predictable coward at that.

    If all countably infinite sets had the same cardinality then set subtraction should verify that. Yet it shows the opposite.

    Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise.

  52. 52
    ET says:

    Bijection just proves that both sets are countable. Set subtraction can prove that the number of elements is not the same.

  53. 53
    JVL says:

    What Cantor realised was that IF two sets have the same number of elements then you can match up all the elements from both sets one-for-one, i.e. each element of the first set is matched with one and only one element of the second set and the same in the other direction. So, IF you can show a way to match up two sets in that way then they are the same size. This works for finite and infinite sets. If you can’t perform such a matching then the sets must be of different sizes or cardinalities.

    So, for each positive integer j in the set of all positive integers match it up with 2 x j in the set of positive even integers, the second set. Each positive integer is matched with one and only one even integer in the second set and each element in the second set is matched with one and only one element in the first set. No element of either set is left out. This can only happen if both sets have the same number of elements. So the sets are the same size.

  54. 54
    JVL says:

    ET, 51: They are your opinions. Set subtraction proves that what you are saying is nonsense. So you ignore it.

    Your “set subtraction” does not apply. You want infinite sets to work the same as finite sets and they don’t.

    No one uses the concept under discussion. No one.

    Just because you don’t doesn’t mean no one does.

    Cantor didn’t prove anything. My arguments are spot on. My example proves that Jerad cannot think.

    Can you find a fault with Cantor’s proofs?

    And as predicted Jerad retreats to “set theory”. You are a coward, Jerad. And a predictable coward at that.

    Set Theory is an important and foundation area of mathematics. You can take classes just on Set Theory.

    If all countably infinite sets had the same cardinality then set subtraction should verify that. Yet it shows the opposite.

    Your “set subtraction” doesn’t verify it because “set subtraction” doesn’t apply for infinite sets.

    Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise.

    I don’t want to be rude but no mathematician agrees with you because they understand the work that Cantor did was correct.

    Bijection just proves that both sets are countable. Set subtraction can prove that the number of elements is not the same.

    Still incorrect. All countably infinite sets have the same cardinality.

  55. 55
    JVL says:

    If there are more positive integers than positive even integers then it should be impossible to match them up one-for-one so that each element of each set has a unique partner in the other set. But you can find such a pairing so the sets must be the same size.

    It’s the same with any pair of infinite sets: if you can match the elements up one-for-one then the sets must be the same size. That’s what Cantor realised and it works for finite as well as infinite sets.

  56. 56
    ET says:

    JVL:

    Your “set subtraction” doesn’t verify it because “set subtraction” doesn’t apply for infinite sets.

    That is one of the most stupid things that I have ever read. At least with my method set theory, that foundation of mathematics, is consistent from bottom to top.

    No one uses the concept under discussion. No one. That means no one, Jerad. Not you nor anyone else.

    Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise. So what does the coward do? Throw out moar asinine innuendos. People see what you are doing, Jerad. No one is fooled.

    With my methodology we have consistency from the bottom to the top. We have the SAME matching criteria. We have the SAME set subtraction methodology. And, where applicable, the bijection formula becomes the relative cardinality.

    And guess what? Bridges won’t fail. The Moon’s orbital dynamics won’t change. And it will give mathematicians something to do- find the relative cardinalities of all countably infinite sets.

    But Jerad prefers to live in the 19th century.

  57. 57
    ET says:

    JVL:

    If there are more positive integers than positive even integers then it should be impossible to match them up one-for-one so that each element of each set has a unique partner in the other set.

    That doesn’t follow. I would expect all countably infinite sets to be able to show bijection. Also the positive integers already have a derived/ natural match with the even integers. Yours need to contrive a matching formula.

  58. 58
    JVL says:

    ET, 56: That is one of the most stupid things that I have ever read. At least with my method set theory, that foundation of mathematics, is consistent from bottom to top.

    Then how is it I can match the set of positive integers one-for-one with the set of positive even integers? If one set is bigger I shouldn’t be able to do that but I can.

    No one uses the concept under discussion. No one. That means no one, Jerad. Not you nor anyone else.

    You’re not a mathematicians so you are unaware of its use.

    Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise. So what does the coward do? Throw out moar asinine innuendos. People see what you are doing, Jerad. No one is fooled.

    If anyone wants to look it up they will find out who is correct. No mathematician uses relative cardinalities. Not one. Because there’s no point: all countably infinite sets are the same size. And if you disagree with Cantor’s work then please, by all means, point out a flaw.

    With my methodology we have consistency from the bottom to the top. We have the SAME matching criteria. We have the SAME set subtraction methodology. And, where applicable, the bijection formula becomes the relative cardinality.

    If you want to propose a different system then do some work and publish it. See if anyone likes it.

    And guess what? Bridges won’t fail. The Moon’s orbital dynamics won’t change. And it will give mathematicians something to do- find the relative cardinalities of all countably infinite sets.

    The mathematicians are plenty busy already. And it’s still true that there are just as many positive even integers as there are positive integers.

    But Jerad prefers to live in the 19th century.

    In mathematics true things stay true. The Pythagorean theorem was proven over 2000 years ago and is still true. Newton and Leibnitz invented Calculus and it’s still true. I’m very happy to stick with stuff that’s true no matter how old it is.

  59. 59
    JVL says:

    ET, 57: That doesn’t follow. I would expect all countably infinite sets to be able to show bijection.

    You can show a bijection between any pair of countably infinite sets. If you can’t then one is not countably infinite.

    Also the positive integers already have a derived/ natural match with the even integers. Yours need to contrive a matching formula.

    Doesn’t matter, if you can find one they are the same size. That’s the key. Any one-for-one matches shows the sets are the same size. Sometimes there’s more than one one-for-one matching but any one will do.

  60. 60
    Ed George says:

    JVL

    Something we can definitely agree on!! Who thought taking it away was a good idea?

    Perhaps it was an attempt to get rid of the recurring problem of the comments list n to being updated.

  61. 61
    Ed George says:

    Can we change this discussion to something else? Maybe nested hierarchies, or frequency = wavelength?

  62. 62
    ET says:

    JVL:

    Then how is it I can match the set of positive integers one-for-one with the set of positive even integers?

    Look, Jerad, you should have learned how to count by the first grade.

    You’re not a mathematicians so you are unaware of its use.

    It’s been years and you have been unable to produce anything. You are just unaware. You you are clearly just a bluffing coward.

    Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise. Moar cowardly nonsense doesn’t refute what I said.

    The true thing is that set subtraction can prove if one countably infinite set has more elements than another countably infinite set.

    And derived vs contrived does matter. Natural vs made-up matters. Consistency is they key with respect to mathematics. But Jerad prefers the 19th century.

  63. 63
    Jim Thibodeau says:

    @JVL there is a lot of entertainment in Alternative Math. ;-D

  64. 64
    ET says:

    “Ed George”:

    Maybe nested hierarchies, or frequency = wavelength?

    You don’t understand either of those concepts. 😛

  65. 65
    ET says:

    Cardinality refers to the number of elements in a set. Some define it as the number of distinct elements within a set. So if set A = {all positive integers}, set B = {all positive even integers} and set C = {all positive odd integers}, then A-B=C proves that set A has more distinct elements than sets B and C.

    Basic. Set. Mathematics. All naturally derived.

  66. 66
    john_a_designer says:

    What does an appeal to an infinite regress of contingent causes really prove? The answer: Nothing, because you can never prove that such a series exists and even if we assume that it exists, it explains nothing.

    The following is an argument I’ve developed for the existence of a transcendent, self-existent mind (God) which I think is a logical defeater for the idea that an infinite regress of “natural” causes is a good explanation for our existence.

    (1) Everything that begins to exist is contingent.

    (2) Anything that is contingent has an explanation for its existence. (It must be caused by something else.)

    (3) If the universe is contingent it has an explanation for its existence.

    (4) If the universe began to exist it must be contingent.

    (5) However, it is logically possible that something exists which is not contingent.

    (6) If such a being exists it exists necessarily. In other words, it is eternal or self-existent.

    (7) A necessary or self-existent being is not explained by anything else.

    Conclusion #1: Therefore, only a necessarily existing being could be the ultimate explanation for everything else.

    Conclusion #2: Therefore an infinite regress of contingent causes can never reach an ultimate explanation.

    Some implications:

    A necessary or self-existing being must have causal power. If it is the cause of the universe it must have sufficient power to cause the universe.

    It must have volitional intentionality. In other words, it does not need to create anything, it freely decides or chooses to create.

    It must be transcendent due to the fact that it is not contingent.

    Therefore, it must have mind and intelligence as well as personal self-consciousness.
    This idea fits very nicely with a basic classical conception of God.

    In other words, if something is contingent then it cannot be necessary. If a necessary being exists it cannot be contingent. If it is even logically possible for the universe to be contingent how can we claim that it is necessary? In other words, if it is logically possible for the universe to be contingent then it cannot be logically necessary for it to be ontologically necessary. If a transcendent necessary being exists then it is logically necessary that it is ontologically necessary.

  67. 67
    JVL says:

    ET, 62: Look, Jerad, you should have learned how to count by the first grade.

    I’m very good at counting. But you can’t count to infinity.

    It’s been years and you have been unable to produce anything. You are just unaware. You you are clearly just a bluffing coward.

    It’s not my fault you don’t understand what’s been shown to you.

    Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise. Moar cowardly nonsense doesn’t refute what I said.

    What I’ve said is correct and can easily be verified by anyone checking. And it absolutely refutes what you’re saying.

    The true thing is that set subtraction can prove if one countably infinite set has more elements than another countably infinite set.

    Nope, set subtraction doesn’t work with infinite sets. If you have the positive integers, a countably infinite set, and you take away the positive even integers, another countably infinite set, you get a third countably infinite set, the positive odd numbers. All three sets continue without end. You cannot say one set has more elements than another. You can take all three sets and match them up so that no element of any set is left out of being matched which means they all have the same number of elements. It’s easy really.

    And derived vs contrived does matter. Natural vs made-up matters. Consistency is they key with respect to mathematics. But Jerad prefers the 19th century.

    Show a reference that upholds your claim that “derived” is inferior to “contrived”. Or even show a reference that defines “contrived” in a mathematical context. Show a reference that supports your idea of relative cardinality between countably infinite sets. If you’re right you should be able to find sources that support your ideas. I’ll wait.

    I prefer being right, no matter when the mathematics was proven.

    Cardinality refers to the number of elements in a set. Some define it as the number of distinct elements within a set. So if set A = {all positive integers}, set B = {all positive even integers} and set C = {all positive odd integers}, then A-B=C proves that set A has more distinct elements than sets B and C.

    Not with infinite sets. If you take the positive integers, a countably infinite set, and add the element “0” you still have a countably infinite set. You think that you would have increased the cardinality. By how much? By one? What’s infinity plus one? It’s still infinity. “Set subtraction” does not work with infinite sets. To use the other example: the positive integers take away the positive even integers does not have half the elements as before. Infinity divided by two is still infinity.

    Infinity + 1 = infinity

    infinity x 2 = infinity

    infinity ÷ 2 = infinity

    infinity + infinity = infinity

    the square root of infinity = infinity

  68. 68
    ET says:

    Jerad, you are a liar. No one showed me anything pertaining to people using the concept of all countably infinite sets have the same cardinality.

    You are a coward for refusing to answer my questions.

    Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise. Moar cowardly nonsense doesn’t refute what I said.

    Everything Jerad has said about that has been a lie,

    Nope, set subtraction doesn’t work with infinite sets.

    That’s pure stupidity.

    Show a reference that upholds your claim that “derived” is inferior to “contrived”.

    Derived is always the best route.

    Cardinality refers to the number of elements in a set. Some define it as the number of distinct elements within a set. So if set A = {all positive integers}, set B = {all positive even integers} and set C = {all positive odd integers}, then A-B=C proves that set A has more distinct elements than sets B and C.

    Not with infinite sets.

    Opinions don’t count. And opinion is all that you have.

    Set subtraction works with all sets.

  69. 69
    ET says:

    Jerad wants references but he will NEVER provide a reference that says set subtraction cannot be used on infinite sets. He will NEVER provide a reference that shows people using the concept of all countably infinite sets having the same cardinality. And he will never support his claim that infinite sets do not work as I have said.

    And to top it all off Jerad refuses to answer my questions. All of that proves that Jerad doesn’t know what he is talking about.

  70. 70
    JVL says:

    ET, 68: Jerad, you are a liar. No one showed me anything pertaining to people using the concept of all countably infinite sets have the same cardinality.

    Clearly you haven’t studied axiomatic set theory. Or understood the material I have linked to.

    You are a coward for refusing to answer my questions.

    I have. I showed you links to proofs that the cardinality of the positive even integers is the same as the cardinality of the positive integers. I’ve linked to articles that discuss the foundational nature of set theory (including the trivial result mentioned). I’ve agreed that if you count the way you want to and stop at any time then one counter will be twice the other. But that’s a finite example, you stopped someplace, and you can’t count to infinity.

    Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise. Moar cowardly nonsense doesn’t refute what I said.

    You can choose to ignore what’s in every single textbook on advanced Set Theory if you wish. You can ignore the material I’ve provided links to. You can ignore lots of other resources that a simple internet search will bring up. It’s your choice.

    Everything Jerad has said about that has been a lie,

    Nope. Check out any textbook on Set Theory. You don’t even have to buy one; just go to your local university library and go to the math section and find one.

    That’s pure stupidity.

    That’s the way it works.

    Derived is always the best route.

    It doesn’t matter how you find a one-for-one matching. If you can find one then the two sets have the same cardinality. There is no “derived vs contrived” condition or preference. Look in any Set Theory text book.

    Cardinality refers to the number of elements in a set. Some define it as the number of distinct elements within a set. So if set A = {all positive integers}, set B = {all positive even integers} and set C = {all positive odd integers}, then A-B=C proves that set A has more distinct elements than sets B and C.

    Yes for finite sets but not for infinite sets.

    Opinions don’t count. And opinion is all that you have.

    I’ve got well known and well established mathematics on my side.

    Set subtraction works with all sets.

    Not with the cardinality of infinite sets.

    Jerad wants references but he will NEVER provide a reference that says set subtraction cannot be used on infinite sets. He will NEVER provide a reference that shows people using the concept of all countably infinite sets having the same cardinality. And he will never support his claim that infinite sets do not work as I have said.

    That”s ’cause no one uses set subtraction with infinite sets! Go check out any textbook on Set Theory. And I have provided references for the other things mentioned. If you didn’t understand them that’s not my fault.

    And to top it all off Jerad refuses to answer my questions. All of that proves that Jerad doesn’t know what he is talking about.

    I’ve answered, you just don’t like the answers.

    What I am saying is easily found in any Set Theory textbook and on many, many online resources. No one uses set subtraction for infinite sets because it doesn’t work. The cardinality of an infinite set is not a number which is why you don’t get relative cardinalities.

    You can easily find material that supports what I am saying. You cannot find any reputable mathematical resource that back up what you are saying.

  71. 71
    ET says:

    Wow, moar stupidity and still the refusal to answer my questions.

    Set subtraction works for all sets. There isn’t anything in any math textbook that says otherwise.

    Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise.

    Jerad has NOT presented anything that says anything contrary to what I have said about infinity.

  72. 72
    ET says:

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    My example typifies collecting items for a set. Jerad cannot deal with reality and it shows.

  73. 73
    ET says:

    JVL:

    I’ve linked to articles that discuss the foundational nature of set theory

    And that proves that you are clueless with respect to what we are discussing. So perhaps you should just stop with your bluffing equivocation already.

  74. 74
    JVL says:

    ET: 71: Wow, moar stupidity and still the refusal to answer my questions.

    I did actually.

    Set subtraction works for all sets. There isn’t anything in any math textbook that says otherwise.

    Find one that uses it on infinite sets.

    Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise.

    Find anyone or any textbook that uses your approach. They don’t exist. Because your method doesn’t work. Which is why you will never find any mathematics supporting your view.

    Jerad has NOT presented anything that says anything contrary to what I have said about infinity.

    I guess you don’t understand the math resources I linked to.

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    Any point in time will be finite that’s why what you’re saying doesn’t work for infinity. It only works for particular finite points in the future. At any point in the future one counter will be twice the other. But the two sets have the same number of elements which is not dependent on the way you count them.

    My example typifies collecting items for a set. Jerad cannot deal with reality and it shows.

    Sure, collecting items for a finite set. But not for an infinite set. You cannot collect items forever. But Cantor figured out a way to work with sets that never end. It was very controversial at the time. But eventually mathematicians realised he was right.

  75. 75
    JVL says:

    ET: And that proves that you are clueless with respect to what we are discussing. So perhaps you should just stop with your bluffing equivocation already.

    It’s not my fault you don’t understand axiomatic Set Theory.

  76. 76
    ET says:

    I understand your cowardly false accusations, Jerad.

    Jerad cannot find any reference that says set subtraction cannot be used on infinite sets. That means what he says about it is BS.

    Any point in time will be finite that’s why what you’re saying doesn’t work for infinity

    Jerad can’t even read for comprehension! Why would anyone believe what you say, JVL?

    But the two sets have the same number of elements which is not dependent on the way you count them.

    When do they have the same number of elements? Please show your work or shut up.

    You cannot collect items forever.

    Exactly why an infinite set is total BS.

    It was very controversial at the time.

    It was first proposed by Galileo.

  77. 77
    ET says:

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    Notice the LAST sentence: Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    Your ignorance is not an argument, Jerad.

  78. 78
    ET says:

    And we are still stuck on the main point- that being no one uses the concept that all countably infinite sets for anything. It is meaningless to the real world. And Jerad cannot find anything that refutes that claim. So he is forced to attack me from across the sea. I call that cowardice.

  79. 79
    ET says:

    Ooops- And we are still stuck on the main point- that being no one uses the concept that all countably infinite sets have the same cardinality for anything.

  80. 80
    JVL says:

    ET: I understand your cowardly false accusations, Jerad.

    It’s clear you don’t understand axiomatic set theory. That’s not a value judgement; I have lots of friends who don’t understand it either.

    Jerad cannot find any reference that says set subtraction cannot be used on infinite sets. That means what he says about it is BS.

    Nobody spend hours and hours generating lists of things you shouldn’t do. What they do do is show you how to deal with things correctly. As I said, read any axiomatic Set Theory textbook.

    And: you haven’t been able to find any textbook that uses “set subtraction” for infinite sets. Gee, if nobody uses it . . .

    Jerad can’t even read for comprehension! Why would anyone believe what you say, JVL?

    Because what I’m saying is backed up by any textbook on axiomatic set theory.

    When do they have the same number of elements? Please show your work or shut up.

    Two sets have the same number of elements (or are the same size) when they can be put into one-for-one correspondence with each other so that every element of each set is matched with one and only one element of the other set. That works for finite as well as infinite sets. I’ll show you for the two sets in question:

    set J = the positive integers, set E = the positive even integers.

    Match “1” from J (its first element when listed in ascending numerical order) with “2” from E (its first element)
    Match “2” from J with “4” from E
    Match “3” from J with “6” from E and so on.

    If you pick any element of either set I can tell you what its matched with in the other set. Nothing is left out.

    Each element of J has one and only one match in E. Each element in E has one and only one match in J. No element of either set is left out. That can only happen if the sets have the same number of elements. QED

    Exactly why an infinite set is total BS.

    Then why are you arguing about them?

    It was first proposed by Galileo.

    Was it? Anyway, Cantor did the real rigorous work in the late 1800s.

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    At any given point one counter will be double the other. But points are finite. You cannot count up to infinity so no matter when you compare the counters (when being a particular finite time) one will be double the other. But the sets still have the same number of elements as illustrated above.

    Notice the LAST sentence: Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    You cannot count for or into infinity. You’ll never get there.

    Your ignorance is not an argument, Jerad.

    At least I understand axiomatic set theory which is back up by every textbook on the subject.

    And we are still stuck on the main point- that being no one uses the concept that all countably infinite sets for anything. It is meaningless to the real world. And Jerad cannot find anything that refutes that claim. So he is forced to attack me from across the sea. I call that cowardice.

    Whether you think it’s useful or not it’s still true. I think it’s very useful in mathematics. You’ve not studied that kind of mathematics so you don’t see the use.

  81. 81
    ET says:

    What is clear is that Jerad is a coward who cannot support the trope he spews.

    You cannot count for or into infinity. You’ll never get there.

    No shit. But thanks for proving that you can’t even grasp the basic terminology.

    Set subtraction is OK to use on infinite sets. No one says you can’t. No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept.

    There is already a matching concept that is used, Jerad. It matches the elements that are the SAME in both sets. It is used to determine if one set is a proper subset of another. And it is used with infinite sets for that same purpose.

  82. 82
    JVL says:

    ET, 81: What is clear is that Jerad is a coward who cannot support the trope he spews.

    Check any textbook on axiomatic set theory. Check Wikipedia. Lots of places will uphold what I am saying.

    No shit. But thanks for proving that you can’t even grasp the basic terminology.

    Since you can’t count to infinity you can’t look at your counters at infinity.

    Set subtraction is OK to use on infinite sets. No one says you can’t. No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept.

    No one uses it because it doesn’t work.

    There is already a matching concept that is used, Jerad. It matches the elements that are the SAME in both sets. It is used to determine if one set is a proper subset of another. And it is used with infinite sets for that same purpose.

    I agree that the set of positive even integers is a subset of the set of positive integers; that’s not in contention. In fact there is a theorem which says that a countably infinite set will have a countably infinite subset. No problem with that.

    BUT they are still the same size. Math can get a bit weird.

    Anyway, IF the set of positive integers is larger than the set of positive even integers then there should be an element of the set of positive integers that is not matched to an element of the positive even integers. Using my matching scheme above can you find an element of set J that is unmatched with an element of set E. If you can’t find one then the sets are the same size. Simple.

    And, again, there is no “contrived vs derived” criteria so don’t play that card. I’ve found a matching that I claim proves the two sets have the same number of elements. If you think they don’t then you can easily prove me wrong by finding an element of either set that does not have a “partner” in the other set. That’s it. That’s all you have to do to prove my matching is bogus.

  83. 83
    ET says:

    JVL:

    Since you can’t count to infinity you can’t look at your counters at infinity.

    Oh my. Your inability to follow along is priceless.
    No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept.

    No one uses it because it doesn’t work.

    Thank you.

    Anyway, IF the set of positive integers is larger than the set of positive even integers then there should be an element of the set of positive integers that is not matched to an element of the positive even integers.

    And there are. The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    And that you can’t understand derived vs contrived doesn’t mean anything.

    And look, Jerad, just because I disagree with an insignificant part of set theory doesn’t mean I don’t understand set theory. It is exactly because I understand it that I say what I do. And all you can do is parrot the 19th century.

  84. 84
    ET says:

    Game. Set. Match.

    No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept.

    JVL:

    No one uses it because it doesn’t work.

  85. 85
    JVL says:

    ET, 83: Oh my. Your inability to follow along is priceless.

    I don’t mind being in line with actual axiomatic set theory.

    No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept.

    You haven’t studied axiomatic set theory so you don’t know how it’s used. And it’s usefulness has nothing to do with its truth. It is true.

    And there are. The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    Fine, name a positive integer that is not matched with a positive even integer in my scheme.

    And that you can’t understand derived vs contrived doesn’t mean anything.

    Because it’s not a mathematical issue. You just made it up. There are no references in any mathematical publication to such a thing.

    And look, Jerad, just because I disagree with an insignificant part of set theory doesn’t mean I don’t understand set theory. It is exactly because I understand it that I say what I do. And all you can do is parrot the 19th century.

    Clearly you don’t or you wouldn’t be saying the things you are saying. In mathematics it doesn’t matter when a result was proven; once it’s proven it’s proven. it’s still true. Euclid’s Elements are still true and they are a lot older than Cantor’s work.

    No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept.

    You haven’t studied axiomatic set theory so you don’t know how it’s used.

    And, again, if you think the set of positive integers is larger than the set of positive even integers then, under my scheme explained above, you should be able to specify a positive integer not matched with a positive even integer. Find one and you win.

  86. 86
    ET says:

    You haven’t studied axiomatic set theory so you don’t know how it’s used.

    Yes I have and yes I do. So shut up and stop being such a cowardly loser.

    No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept.

    And all Jerad can do in the face of that is to attack me. What a coward.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    Another fact that Jerad avoids.

    You haven’t studied axiomatic set theory so you don’t know how it’s used.

    You don’t know how it’s used. You are clearly just a blind parrot who is unable to think for himself.

    But it is all moot, anyway. There can never be a set with infinite elements.

  87. 87
    JVL says:

    ET, 86: Yes I have and yes I do. So shut up and stop being such a cowardly loser.

    Okay, then tell me: do you think the Axiom of Choice is true or false?

    And all Jerad can do in the face of that is to attack me. What a coward.

    I’m not attacking you. Look, if I came onto a forum and claimed that I knew how to handle semi-automatic weapons but it was clear to you that I didn’t you would say so. Of course you would. I’m just saying that, based on what you’ve said on this forum, that you do not understand axiomatic set theory. It’s not a value judgement.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    Yes, this is true. But both sets are still the same size.

    You don’t know how it’s used. You are clearly just a blind parrot who is unable to think for himself.

    Things that are proven in mathematics are true. Always.

    But it is all moot, anyway. There can never be a set with infinite elements.

    Then why are you spending so much time arguing about it?

    And, again, all you have to do to prove me wrong is to find an unmatched element of the positive integers with the positive even integers under my scheme. That’s it. You think the set of positive integers is larger than the set of positive even integers so, under my scheme, there should be an unmatched element of the set of positive integers. All you have to do is to find one, just one, unmatched element. You can bury my arguments with just that one thing. That is how you falsify my (and Cantor’s) ideas. Can you do that?

  88. 88
    ET says:

    JVL:

    I’m just saying that, based on what you’ve said on this forum, that you do not understand axiomatic set theory.

    And I can say the same about you. You clearly don’t understand infinity.

    Then why are you spending so much time arguing about it?

    You are the loser who brought it up. You are the loser who won’t let it go. You are the loser who avoids reality.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    If you can’t understand that then no one can help you.

  89. 89
    ET says:

    No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept.

    And all Jerad can do in the face of that is to attack me. I am OK with that.

  90. 90
    JVL says:

    ET, 88: And I can say the same about you. You clearly don’t understand infinity.

    Actually, according to any axiomatic set theory textbook, I do.

    You are the loser who brought it up. You are the loser who won’t let it go. You are the loser who avoids reality.

    I just want to make sure that anyone who wanders onto this thread on this forum hears the truth.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    Correct. BUT the sets are still the same size. And, guess what: you haven’t been able to find an element of the positive integers that is not matched up with an element of the positive even integers under my scheme. So, the conclusion is: the set have the same number of elements!!

    No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept.

    But, it’s still true.

    And all Jerad can do in the face of that is to attack me. I am OK with that.

    I’ve just been saying what is true.

    AND, so far, you haven’t been able to find an element of the positive integers which is unmatched with and element of the positive even integers (under my scheme) so the conclusion has to be: the set of the positive integers and the set of the positive even integers are the same size!!

  91. 91
    JVL says:

    I think it might time for me to declare a win on this issue: ET doesn’t even seem to be trying to find an element of the positive integers that is unmatched with an element of the positive even integers on a one-for-one basis under my scheme. And if ET or anyone else cannot find an unmatched element then the two sets must have the same number of elements. To deny such a conclusion would be ludicrous.

    BUT, it is true that if ET can, at some point, find an element in the set of all positive integers that is not matched with an element of the positive even integers under my scheme then everything I’ve said could be called into question. I admit that.

    Anyway, for now it’s a win for me but leaving the option open for ET if they choose to pursue the issue.

  92. 92
    ET says:

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    Correct. BUT the sets are still the same size.

    Impossible. Infinity isn’t magic.

    See, that’s the problem. You are forced into playing mental gymnastics while ignoring reality.

    And why would I use your contrived scheme when that is the very thing I am saying is the problem?

    You ignore the reality that there can never be a set with infinite elements. Then you contrive a scheme that does one thing- show that a set is countably infinite- and use it for something twisted- that the cardinality is therefore the same.

    My point about the fact that no one uses the concept is to show that no one knows if it is true or not. Just baldly saying it is doesn’t mean anything.

    At least with my scheme we have consistency from bottom to the top. No mental gymnastics and bald declarations required. Just 21st century thinking.

  93. 93
    ET says:

    I think it might time for me to declare a win on this issue:

    BWAAAAAAAAAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA

    Jerad is running around his flat with his hands over his head “I won. I won.”

    Only if you ignore reality, Jerad.

    I can find unmatched numbers using the standard set scheme used to identify proper subsets.

    So I declare that Jerad is a LOSER.

  94. 94
    Jim Thibodeau says:

    JVL your patience is tremendous.

  95. 95
    ET says:

    Why would I use your contrived scheme when that is the very thing I am saying is the problem?

  96. 96
    ET says:

    Jim Thibodeau- You cluelessness is becoming legendary.

  97. 97
    JVL says:

    ET, 92: Impossible. Infinity isn’t magic.

    That’s the way it works.

    See, that’s the problem. You are forced into playing mental gymnastics while ignoring reality.

    I’m just telling you how the math works out.

    And why would I use your contrived scheme when that is the very thing I am saying is the problem?

    It works, it proves the point.

    You ignore the reality that there can never be a set with infinite elements. Then you contrive a scheme that does one thing- show that a set is countably infinite- and use it for something twisted- that the cardinality is therefore the same.

    This is about the mathematics. I’m telling you how it works. Why are you arguing if you think it’s all rubbish?

    My point about the fact that no one uses the concept is to show that no one knows if it is true or not. Just baldly saying it is doesn’t mean anything.

    It is true. Check any axiomatic set theory textbook.

    At least with my scheme we have consistency from bottom to the top. No mental gymnastics and bald declarations required. Just 21st century thinking.

    No one uses your scheme because it doesn’t work.

    Jerad is running around his flat with his hands over his head “I won. I won.”

    I have won. I have shown a matching between the positive integers and the positive even integers that shows that the two sets have the same number of elements. And you have, as yet, been unable to find a counter example.

    Only if you ignore reality, Jerad.

    This is about the mathematics.

    I can find unmatched numbers using the standard set scheme used to identify proper subsets.

    Under my scheme show me a positive integer that is unmatched with a positive even integer. There is no standard scheme, you made that up. What counts is finding a matching, any matching. I’ve done that.

    So I declare that Jerad is a LOSER.

    Find a positive integer that is not matched with a positive even integer under my scheme. That’s all you have to do. If you can do that then you win.

  98. 98
    JVL says:

    ET: Why would I use your contrived scheme when that is the very thing I am saying is the problem?

    Because it works. It exhibits a one-to-one matching between the positive integers and the positive even integers. That establishes that the two sets have the same number of elements.

    Again, there is NO “contrived vs derived” criteria. That is just made up. You cannot show any support for that.

  99. 99
    ET says:

    JVL:

    That’s the way it works.

    No, it does not work like magic. You are clueless.

    Why would I use your contrived scheme when that is the very thing I am saying is the problem?

    Are you mentally deficient?

    No one uses your scheme because it doesn’t work.

    What does that mean, Jerad? My scheme is the standard scheme used to determine if one set is a proper subset of another. It is already used and working. No need to contrive anything. No need for mental gymnastics. No need to say that math doesn’t need to reflect reality.

    You can’t win by ignoring reality, Jerad.

  100. 100
    ET says:

    : Why would I use your contrived scheme when that is the very thing I am saying is the problem?

    Because it works.

    It works to show that two sets are countable. That is all it establishes. Set subtraction shows if two sets have the same cardinality or not. Using the STANDARD matching method already used should be the way to go. It is naturally derived.

  101. 101
    JVL says:

    ET: No, it does not work like magic. You are clueless.

    I know the mathematics.

    Why would I use your contrived scheme when that is the very thing I am saying is the problem?

    You just made up the contrived vs derived issue. It doesn’t exist. Deal with the situation: I’ve found a matching between the positive integers and the positive even integers which shows the two sets are the same size.

    Are you mentally deficient?

    I’m inline with accepted and established mathematics. Are you?

    What does that mean, Jerad? My scheme is the standard scheme used to determine if one set is a proper subset of another. It is already used and working. No need to contrive anything. No need for mental gymnastics. No need to say that math doesn’t need to reflect reality.

    Your scheme does not carry on to infinite sets. Cantor figured out a new way of handling that. And now all mathematicians accept that. There is no “standard” scheme. In mathematics everything is fair game.

    You can’t win by ignoring reality, Jerad.

    You can’t win by ignoring the established and accepted mathematics.

    It works to show that two sets are countable. That is all it establishes. Set subtraction shows if two sets have the same cardinality or not. Using the STANDARD matching method already used should be the way to go. It is naturally derived.

    There is no STANDARD matching method. You’re making that up. Being “naturally” derived is not a criteria.

    I have demonstrated a way to match every element of the positive integers with every element of the positive even integers on a one-for-one basis, i.e. every element of each set is matched with one and only one element of the other set. No element of either set is left out. That can only happen if each set has the same number of elements. It works for finite as well as infinite sets.

    If you want to prove that I am wrong then find a counter example to what I am saying. If you can do that then you win.

  102. 102
    ET says:

    JVL:

    I know the mathematics.

    Sounds like you have yourself convinced. But you don’t understand infinity.

    You just made up the contrived vs derived issue.

    It’s there. I didn’t do it. I just observed it.

    There is a NATURALLY DERIVED, existing method to match elements of two sets. It is used throughout set theory to determine if one set has elements contained in another set. You can also use it to determine if one set is a proper subset of another set. It works. It has been used by Cantor, even.

    You can’t win by ignoring the established and accepted mathematics.

    I can if that is what I am fighting and no one can demonstrate that I am wrong without referring back to the very thing being debated!

    How daft are you to keep doing that? Seriously, if there was a judge you would have been held in contempt.

    There is a standard matching method. It is used exactly as I said. Anyone familiar with set theory knows that I am right.

  103. 103
    ET says:

    JVL:

    I’m inline with accepted and established mathematics. Are you?

    I am saying it is wrong and isn’t established. And I think it’s funny that all you can do is to keep referencing the very thing I am debating as if it refutes me.

    Wanker 101

  104. 104
    Jim Thibodeau says:

    JVL It’s been estimated that there are 80,000 mathematicians in the world. 15,000 alone belong to that major society. Certainly ET can find a handful who agree with him. Certainly if his argument has any merit all 80,000 don’t disagree with him.

  105. 105
    JVL says:

    ET: Sounds like you have yourself convinced. But you don’t understand infinity.

    Check any textbook on axiomatic set theory.

    It’s there. I didn’t do it. I just observed it.

    Nope, derived vs contrived is not a real mathematical issue, and you have not been able to show that it is.

    There is a NATURALLY DERIVED, existing method to match elements of two sets. It is used throughout set theory to determine if one set has elements contained in another set. You can also use it to determine if one set is a proper subset of another set. It works. It has been used by Cantor, even.

    Citation please.

    I can if that is what I am fighting and no one can demonstrate that I am wrong without referring back to the very thing being debated!

    I’m the one that demonstrated a one-for-one mapping between the positive integers and the positive even integers which you have been unable to break. You keep forgetting to admit that.

    How daft are you to keep doing that? Seriously, if there was a judge you would have been held in contempt.

    Not me. You’re the one who can’t break my matching of the positive integers and the positive even integers. You’re not even trying.

    There is a standard matching method. It is used exactly as I said. Anyone familiar with set theory knows that I am right.

    Citation please. Show us a reference to establish this. AND, meanwhile, you haven’t broken my matching between the positive integers and the positive even integers. Looks like you can’t. Guess I win then.

    I am saying it is wrong and isn’t established. And I think it’s funny that all you can do is to keep referencing the very thing I am debating as if it refutes me.

    Looks like you can’t break my matching between the positive integers and the positive even integers. You keep trying to avoid it but you haven’t even tried. I definitely win.

    Wanker 101

    Show the world that my matching between the positive integers and the positive even integers is wrong. You haven’t done so. It looks like you can’t. Looks like I win.

  106. 106
    JVL says:

    Jim Thibodeau: It’s been estimated that there are 80,000 mathematicians in the world. 15,000 alone belong to that major society. Certainly ET can find a handful who agree with him. Certainly if his argument has any merit all 80,000 don’t disagree with him.

    ET hasn’t even tried to find any mathematicians that agree with him. He’s just making stuff up. You’re welcome to help him. Good luck.

  107. 107
    ET says:

    JVL:

    I’m the one that demonstrated a one-for-one mapping between the positive integers and the positive even integers which you have been unable to break.

    See- you are a moron. I said that I would expect such a thing given countable sets.

    There is a NATURALLY DERIVED, existing method to match elements of two sets. It is used throughout set theory to determine if one set has elements contained in another set. You can also use it to determine if one set is a proper subset of another set. It works. It has been used by Cantor, even.

    Citation please.

    Every textbook on set theory.

    And again, seeing that I am debating what the mainstream says, you cannot use what they say to refute me.

    You think that infinity is magic. You don’t have any clue.

    You can’t find a fault with the standard matching scheme used to demonstrate one set contains elements of another. You can’t find a fault with the standard matching scheme used to determine if one set is a proper subset of another. That is the foundation of set theory.

    You lose.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    That means there are more elements in one of those sets. And all you can do is call “magical infinity”.

    Wanker

  108. 108
    ET says:

    JVL:

    ET hasn’t even tried to find any mathematicians that agree with him.

    I am going against what they say. And all you can do is blindly parrot what they say as if that helps.

    Yours is the most desperate and ignorant tactic ever used. “I will use the premise being debated to win the debate!”

  109. 109
    ET says:

    JVL’s tactic is like someone referring a map that someone else pointed out is wrong. “No, this map is my proof!” Umm, your map is wrong. “No, take a look at my map!” Your map is wrong. “But I have a map!”

  110. 110
    JVL says:

    ET: See- you are a moron. I said that I would expect such a thing given countable sets.

    That proves that the two sets have the same number of elements!

    There is a NATURALLY DERIVED, existing method to match elements of two sets. It is used throughout set theory to determine if one set has elements contained in another set. You can also use it to determine if one set is a proper subset of another set. It works. It has been used by Cantor, even.

    What I’ve done is prove that both sets have the same number of elements. And you haven’t found a counter example. There is no rule for “derived vs contrived”. You made that up. It’s not in any textbook.

    Every textbook on set theory.

    No. You made it up.

    And again, seeing that I am debating what the mainstream says, you cannot use what they say to refute me.

    I have demonstrated a one-for-one pairing between two sets which can only happen if the two sets have the same number of elements. If you think one set has more elements then you should be able to find an unmatched element in that set. Simple. You haven’t done that yet.

    You think that infinity is magic. You don’t have any clue.

    It’s not magic. Cantor figured out how to work with it.

    You can’t find a fault with the standard matching scheme used to demonstrate one set contains elements of another. You can’t find a fault with the standard matching scheme used to determine if one set is a proper subset of another. That is the foundation of set theory.

    Now you’re not paying attention. I’ve agreed that the set of all positive even integers is a proper subset of the positive integers. I’ve also found a matching scheme that proves that both sets have the same number of elements. I can use any matching scheme I like.

    You lose.

    Nope, I’ve done exactly what I said could be done.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    Yup, and all three sets have the same cardinality. I can find one-for-one pairings that prove it.

    That means there are more elements in one of those sets. And all you can do is call “magical infinity”.

    Wanker

    That’s how the math works. Your abuse is telling . . .

    I am going against what they say. And all you can do is blindly parrot what they say as if that helps.

    Yes you are going against known and accepted mathematics and that’s why you’re wrong. AND I’ve proved that both sets are the same size and you have failed to show one is larger.

    Yours is the most desperate and ignorant tactic ever used. “I will use the premise being debated to win the debate!”

    The premises are standard and accepted mathematics. They work. You haven’t found a fault with them. You proposed an alternative which doesn’t work. You can’t even use it for some simple sets. It’s broken.

    Show where my set matching fails. Find a positive integer that is not matched with a positive even integer. That’s all you have to do.

    JVL’s tactic is like someone referring a map that someone else pointed out is wrong. “No, this map is my proof!” Umm, your map is wrong. “No, take a look at my map!” Your map is wrong. “But I have a map!”

    I’ve set up a one-for-one matching between two sets proving that they both have the same number of elements. You have yet to show where the fault is in that. This is not a question of premises or maps. YOU have to show exactly where my conclusion is wrong. When two sets are matched up element for element how can they have different number of elements? You think they do but you cannot find an unmatched element. All you need to do to show my method or premises are wrong is find one unmatched element. That’s it. Simple. If you can’t do that then it’s clear: the sets have the same number of elements. Everything else is just deflection.

  111. 111
    ET says:

    JVL:

    That proves that the two sets have the same number of elements!

    No, it only proves the two sets are countable.

    No. You made it up.

    What? What I said is EXACTLY how proper subsets are found. What I said is exactly how unions are found.

    Clearly you are just an ignorant punk.

    And only a moron would think he/ she can use what is being debated to settle the debate. And here you are.

    There is a NATURALLY DERIVED, existing method to match elements of two sets. It is used throughout set theory to determine if one set has elements contained in another set. You can also use it to determine if one set is a proper subset of another set. It works. It has been used by Cantor, even.

    proper subsets– exactly s I have said

    Unions- set theory– again, exactly as I stated.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    That proves there is more elements in one set. So go pound sand, loser.

  112. 112
    ET says:

    You can’t find a fault with the standard matching scheme used to demonstrate one set contains elements of another. You can’t find a fault with the standard matching scheme used to determine if one set is a proper subset of another. That is the foundation of set theory.

    Unions- set theory

    set theory- subsets and proper subsets

    Exactly as I said. And contrary to Jerad.

    You lose.

  113. 113
    JVL says:

    ET: No, it only proves the two sets are countable.

    Find an unmatched element then!

    And only a moron would think he/ she can use what is being debated to settle the debate. And here you are.

    If I’m wrong find an unmatched element in my scheme. That’s all you have to do.

    There is a NATURALLY DERIVED, existing method to match elements of two sets. It is used throughout set theory to determine if one set has elements contained in another set. You can also use it to determine if one set is a proper subset of another set. It works. It has been used by Cantor, even.

    Doesn’t mean another matching isn’t valid. Find a reference that says you can only use the one you want to use.

    I have no problems with proper subsets and set union. I agreed that the set of positive even integers is a proper subset of the positive integers. But they still have the same cardinality because I can match them up one-for-one.

    You can’t find a fault with the standard matching scheme used to demonstrate one set contains elements of another. You can’t find a fault with the standard matching scheme used to determine if one set is a proper subset of another. That is the foundation of set theory.

    Doesn’t mean I can’t use another one. You find me a reference that says I can only match up identical elements. I’ll wait . . .

  114. 114
    JVL says:

    https://www.mathacademytutoring.com/cardinality-and-countably-infinite-sets/

    There are many sets that are countably infinite, ?, ?, 2?, 3?, n?, and ?. All of the sets have the same cardinality as the natural numbers ?

    This is not under debate by anyone but you. And if you can find an unmatched element in my scheme then you will have proved it all wrong. Can you find an unmatched element?

  115. 115
    Jim Thibodeau says:

    ET hasn’t even tried to find any mathematicians that agree with him. He’s just making stuff up. You’re welcome to help him. Good luck.

    Of course I won’t be helping him, his fake math is gibberish. As is his understanding of biology.

  116. 116
    Truthfreedom says:

    @ 115 Jim Thibodeau

    As is his understanding of biology.

    Asl long as his understanding of biology is not as pathetic as your understanding of basic logic principles, everything will be ok 🙂
    Does the evolutionary religion demand throwing logic out the window? Is it an absolute requirement?
    Because most evos do that. I am curious.

  117. 117
    ET says:

    Again: The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    That proves there is more elements in one set. So go pound sand, loser.

    Thankfully I understand biology and math better than Jimbob ever will.

  118. 118
    ET says:

    It is still super funny that all my detractors can do is reference the very thing being debated to try to settle the debate.

    Only a moron would think he/ she can use what is being debated to settle the debate. And here you are.

    How stupid are you guys?

  119. 119
    JVL says:

    ET: Again: The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set. So go pound sand, loser.

    No, it does not. If the set of positive integers had more elements than the set of positive even integers then in my matching scheme there would be at least one unmatched element. But you haven’t found an unmatched element.

    It is still super funny that all my detractors can do is reference the very thing being debated to try to settle the debate. Only a moron would think he/ she can use what is being debated to settle the debate. And here you are. How stupid are you guys?

    I’ve told you over and over and over again how you can falsify my claims but you haven’t been able to do so. Add to that the fact that many online and published resources agree with what I have been saying.

    There is no real debate. You’re just too embarrassed to admit you got something wrong.

    If you’re right then you should be able to find a counter example. Cand you do that, yes or no? Answer that question and we can end this whole thing.

  120. 120
    ET says:

    Being able to find a one-to-one correspondence only means the sets are countable. That’s it.

    Just because someone can wrongly claim that also means the sets have the same number of elements doesn’t mean anything to me. Well, it means they can’t think for themselves.

    But that is all moot, anyway. There can’t be a set with infinite elements if a set is defined as “a well-defined collection of distinct objects, considered as an object in its own right”.

    So I guess if you can ignore that you can also ignore the reality that says The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set.

    You want to ignore reality and think infinity is magical, fine. Seeing that the concept under debate is useless anyone can say whatever they want and no one can prove them wrong. I mean real proof- not wanker proof.

    BTW, I have always known what the mainstream has said about this. I am saying that it is wrong. So just merely repeating what the mainstream says proves that you are nothing but a good parrot. And thinking that repeating what they say somehow refutes my argument proves that you are clueless.

  121. 121
    JVL says:

    ET: Being able to find a one-to-one correspondence only means the sets are countable. That’s it.

    How can they have a one-to-one correspondence unless they have the same number of elements? And besides, I’ve liked to a theorem (that means it’s been proved) which says that all countable infinite sets have the same cardinality.

    Just because someone can wrongly claim that also means the sets have the same number of elements doesn’t mean anything to me. Well, it means they can’t think for themselves.

    When you can’t find an unmatched element it does mean that.

    But that is all moot, anyway. There can’t be a set with infinite elements if a set is defined as “a well-defined collection of distinct objects, considered as an object in its own right”.

    Wrong again. You said you studied set theory but that’s clearly not the case. The positive integers is a well defined set. Name an object and I can tell whether it’s in the set or not. That’s well defined.

    So I guess if you can ignore that you can also ignore the reality that says The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set.

    Then you should be able to find an unmatched positive integer under my matching scheme. But you haven’t been able to do that. Address that issue and we’re done.

    You want to ignore reality and think infinity is magical, fine. Seeing that the concept under debate is useless anyone can say whatever they want and no one can prove them wrong. I mean real proof- not wanker proof.

    It’s not magical, there are rules and things you can do and things you can’t do. If you think the math and the proofs are wrong then find a mistake or a counter example. Can you do that: yes or no?

    BTW, I have always known what the mainstream has said about this. I am saying that it is wrong. So just merely repeating what the mainstream says proves that you are nothing but a good parrot. And thinking that repeating what they say somehow refutes my argument proves that you are clueless.

    I understand you are aware of what everyone else says. I’m not just repeating it, I get how it works. I’ve taken an actual set theory class and have worked with the rules governing such things. I have created a matching that you can explode if you are able.

    So we’re still down to: can you find an unmatched positive integer in my scheme which matches the positive integers with the positive even integers one-to-one? Yes or no? Either answer will end the whole conversation. Not answering means you either don’t understand the issue (which I don’t believe) or you are too afraid to admit you made a mistake. Answering yes means you have to produce an unmatched positive integer in my scheme. Answering no means we’re done and we can stop discussing this.

    It’s your call.

  122. 122
    ET says:

    JVL:

    How can they have a one-to-one correspondence unless they have the same number of elements?

    Because all you are doing is taking the sets and converting them to the set {1,2,3,4,…}. That means you are no longer dealing with the distinct elements that are actually in the set. But you won’t be able to grasp that.

    The positive integers is a well defined set.

    True but no one can collect infinite elements. So it cannot be a collection.

    Address that issue and we’re done.

    I have. Cantor’s bijection ignores the actual elements.

    It’s not magical, there are rules and things you can do and things you can’t do.

    Nonsense.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set.

    The mistake was made by Cantor. That has always been my point. And all you can do is repeat the mistake as if it means something.

  123. 123
    ET says:

    I use the standard matching used for determining unions, subsets and proper subsets. And using that standard matching the set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    Real. World. Proof.

  124. 124
    JVL says:

    Because all you are doing is taking the sets and converting them to the set {1,2,3,4,…}. That means you are no longer dealing with the distinct elements that are actually in the set. But you won’t be able to grasp that.

    I am showing that they match up one-to-one. And yes, all countably infinite sets can be matched up with the positive integers. THAT’S THE POINT!! It’s the number of elements that is the point of cardinality.

    True but no one can collect infinite elements. So it cannot be a collection.

    It’s a well defined set. Pick something, anything, I can tell you whether it’s in the set or not. That means the definition is clear and unambiguous.

    I have. Cantor’s bijection ignores the actual elements.

    It doesn’t matter what the elements are, what we’re talking about is how many of them there are. That’s the whole discussion.

    Nonsense.

    You said you studied Set Theory but that clearly is not true or you would know what the rules are.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set.

    Then why can I match up the positive even integers with the positive integers one-for-one? You’re not addressing that basic question is just causing this discussion to go on and on and on.

    The mistake was made by Cantor. That has always been my point. And all you can do is repeat the mistake as if it means something.

    Then find an unmatched positive integers in my scheme. That’s all you have to do. Everything else is just diversion. Can you do that, yes or no? You can prove Cantor wrong by finding an unmatched element.

    I use the standard matching used for determining unions, subsets and proper subsets. And using that standard matching the set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well.

    I have never, ever disputed that the even integers are a proper subset of the integers or that the odd integers are a proper subset of the integers or that the even integers union with the odd integers give you the integers. We agree. But because all those sets can be put into a one-to-one correspondence with the positive integers they have the same cardinality. And if you want to say otherwise then you need to find a counter example. In my scheme, you need to find an unmatched positive integer. Can you do that, yes or no?

    Just answer the question.

  125. 125
    JVL says:

    Mathematics is not a spectator sport. It’s like carpentry or hand-to-hand combat or sculpture or dancing or piano playing or football or being a pilot or any other skill which requires practice and experience. You have to get your head around the systems involved. Sometimes you need to learn new ways of thinking and new skills. I can study martial arts in a book all I want, I can watch hours and hours of videos but it all means close to nothing until I actually spend some time learning how to really carry it out..

    Mathematics is actually very deep and, in the last 100 years or so, very, very difficult. And it’s not like other topics where new ideas supersede old ones. What was true for Pythagoras and Euclid is still true. Newtonian physics may have been revised and overtaken but Newtonian mathematics has not suffered the same fate. If you understand mathematics up through the 19th century you are doing very well, most people never get past arithmetic. After Cantor in particular, things got very, very weird and difficult.

  126. 126
    JVL says:

    Oh, and by the way . . . we haven’t even gotten onto the different sizes of infinity. There’s something beyond countably infinite.

    You want to blow your mind? Become a math major. When you get to topology give me a shout. I’ll provide the tea and sympathy.

  127. 127
    EricMH says:

    @ET you made me think a moment with the question: why does the set of positive integers have the same cardinality as the negative and positive integers?

    But, even though they have different numbers, it is still straightforward to come up with a scheme to map all #1) the positive integers to #2) all the numbers in the set of negative and positive integers.

    f(n) = if n is even: -n/2 else: (n+1)/2

    Since that mapping will never be violated, i.e you’ll never find an element in #2 that cannot be inverted to an element in #1 and visa versa, that means the two sets must have the same cardinality. Very counterintuitive.

  128. 128
    Jim Thibodeau says:

    JVL @126 I took so many math classes for fun that if I had taken Rational Analysis I would have also gotten a BA in math. My favorite was abstract algebra. Any suggestions about other good ones?

  129. 129
    JVL says:

    Jim Thibodeau:

    Well, I was always a bit fond of number theory myself but to understand how powerful and amazing math is I can’t recommend complex analysis enough. Beautiful stuff. Rings and Fields . . . I think I would appreciate that stuff more now but at the time . . . .

  130. 130
    ET says:

    Jerad, Your scheme is the very thing being debated. Your scheme works fine for showing the sets are countable. Your scheme for doing that IGNORES the real value of the sets.

    Using the standard scheme for matching- the scheme used throughout set theory for finding unions, subsets and proper subsets, shows there are unmatched elements. And using THAT scheme you cannot show there is a one-to-one correspondence.

    If you can show there is a one-to-one correspondence using that standard scheme I will admit I made a mistake. And if you can’t you are wrong.

  131. 131
    ET says:

    Yes, EricMH. That scheme works fine for showing the two sets are countable. However basic set subtraction and logic shows one set can have more elements than another.

  132. 132
    Jim Thibodeau says:

    Hey, we did rings and fields in abstract algebra! Galois theory too. Permutation groups were my favorite though. I’ve downloaded a 15 lecture set off YouTube about analysis but I haven’t watched it yet.

  133. 133
    ET says:

    Jerad:

    There’s something beyond countably infinite.

    Yes, I know. I have taken the courses.

    Your problem is thinking that because I disagree with Cantor on one irrelevant part of his ramblings, that I don’t know anything about it. But yet you cannot find any fault with my arguments and you can only repeat what is being debated.

  134. 134
    ET says:

    And Jerad, stop lecturing me. It is clear that you don’t understand infinity.

  135. 135
    ET says:

    One more thingy- there is only one infinity. Cantor found there are different densities. And all I am doing is extending that to the countably infinite sets.

    But then again I have been over this with you and you refuse to or cannot grasp it.

  136. 136
    Jim Thibodeau says:

    Definition 1: |A| = |B|
    Two sets A and B have the same cardinality if there exists a bijection from A to B, that is, a function from A to B that is both injective and surjective.

  137. 137
    ET says:

    Earth to Jim Thibodeau- I am saying that definition is incorrect. So if all you can do is keep repeating it you have serious issues.

  138. 138
    ET says:

    Cardinality refers to the number of elements a set contains.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set.

    Until you can deal with that you don’t have anything to refute my claim.

  139. 139
    JVL says:

    ET: Jerad, Your scheme is the very thing being debated. Your scheme works fine for showing the sets are countable. Your scheme for doing that IGNORES the real value of the sets.

    The “value” of the sets (surely you mean the value of the elements of the sets?) is NOT THE POINT. It’s how many elements are in each set. That’s it. I have found a scheme which clearly and unambiguously matches each positive integer with a positive even integer so that no element of either set is left unmatched. It’s simple, it’s easy to understand. That can only happen if each set has the same number of elements.

    Using the standard scheme for matching- the scheme used throughout set theory for finding unions, subsets and proper subsets, shows there are unmatched elements. And using THAT scheme you cannot show there is a one-to-one correspondence.

    Using my scheme there are no unmatched elements. There is nothing wrong with my scheme. Except that you cannot find an unmatched element. There is no “standard scheme”.

    If you can show there is a one-to-one correspondence using that standard scheme I will admit I made a mistake. And if you can’t you are wrong.

    No, you are wrong because you cannot think outside of one scheme. There is nothing wrong with my scheme. It’s valid. You’re the only person who has a problem with it. If you really took a Set Theory course then you know there is no “standard scheme”. And if there is then you should be able to find a reference talking about it. Can you find such a reference?

    Your problem is thinking that because I disagree with Cantor on one irrelevant part of his ramblings, that I don’t know anything about it. But yet you cannot find any fault with my arguments and you can only repeat what is being debated.

    I can find fault with your arguments because you are desperately trying to discredit my scheme for no good reason except that it disproves your idea. There is no standard scheme. Any matching is allowed.

    I have found a way to match up the positive integers with the positive even integers one-to-one so that no element of either set is unmatched. That can only happen if the sets have the same number of elements. If you can find an unmatched element in my scheme then you will be lauded as a mathematical genius, guaranteed. Can you find an unmatched element, yes or no?

    And Jerad, stop lecturing me. It is clear that you don’t understand infinity.

    AGAIN, I have found a way to match up the positive integers with the positive even integers one-to-one so that no element of either set is unmatched with a unique “partner”. That can only happen if the sets have the same number of elements. You disagree and, if you’re right, then you should be able to find an unmatched element in the set with more elements. Can you do that? Yes or No?

    It’s time to stop dodging and trying to weasel out of it. Can you find an unmatched element, yes or no? Everything else is just diversion. Can you find an unmatched element, yes or no?

  140. 140
    JVL says:

    ET: One more thingy- there is only one infinity. Cantor found there are different densities. And all I am doing is extending that to the countably infinite sets.

    So what is your opinion of the continuum hypothesis?

    But then again I have been over this with you and you refuse to or cannot grasp

    We’ll see how you deal with the questions shall we?

    Cardinality refers to the number of elements a set contains.

    Exactly so, that’s why the value of the elements of the sets are not important.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set.

    Then I should not be able to match them up, one-to-one. But I can. And you cannot find an unmatched element.

    Until you can deal with that you don’t have anything to refute my claim.

    I have dealt with it and you have not found a counter example.

  141. 141
    ET says:

    The value is the point.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set.

    If that is true, and it is, then there cannot be the same cardinality. And the way you deal with that is to ignore it.

    You can match them in a one-to-one correspondence only because they are both countable. That you ignore that proves you can’t deal with it.

  142. 142
    ET says:

    I can find fault with your arguments …

    And yet you haven’t. All you can do is repeat what I am saying is incorrect. It’s as if you have Tourette’s

  143. 143
    ET says:

    No one can collect infinite elements. That means there cannot be a set of infinite elements because a set is a collection of elements.

    Jerad still has problems with facts

  144. 144
    JVL says:

    ET: The value is the point.

    No, the number of elements in each set is the point. That’s what cardinality is all about.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set.

    Then why can I match up the positive integers with the positive even integers in a one-to-one fashion so that you cannot find an unmatched element in the set you think is larger?

    If that is true, and it is, then there cannot be the same cardinality. And the way you deal with that is to ignore it.

    I am not ignoring. I am disputing it. I have a method which proves they do have the same cardinality. And I’ve told you over and over and over again how you can prove me wrong. And you have failed to do that.

    You can match them in a one-to-one correspondence only because they are both countable. That you ignore that proves you can’t deal with it.

    ALL countably infinite sets have the same cardinality. I’ve linked to proofs of just that thing. I am not ignoring anything. I am telling you over and over and over again where I disagree with you and how you can prove me wrong.

    And yet you haven’t. All you can do is repeat what I am saying is incorrect. It’s as if you have Tourette’s

    I have explained over and over and over again the basic, accepted, established mathematics involved. I have linked to sources, I have done my best to explain things in various ways to try and get them across. You keep referring to things that are non-existent, like “contrived vs derived” matchings and when I ask you to support your views you can’t do it.

    Once again: I can match up the elements of the positive integers with the positive even integers one-to-one. Every element of each set has a unique partner in the other set. Give me an element of either set and I can easily tell you its partner in the other set. Explain to me how that can happen if the sets do not have the same number of elements in them. Or, even easier, just find an element of either set that does not have a partner in the other set. That’s it. No more diverting. No more trying to call cast aspersions on techniques. My scheme is simple, easy to understand. Under my scheme can you find an unmatched element of either set, yes or no?

    Yes or no? One word would end this whole thing.

  145. 145
    JVL says:

    ET: No one can collect infinite elements. That means there cannot be a set of infinite elements because a set is a collection of elements.

    Jerad still has problems with facts

    So you’ve been arguing about something you don’t think exists? hahahahahahahahahahahahahahahahahahaahhahahahahahahahahahahahahahahahahah

  146. 146
    EricMH says:

    @ET can you provide your proof? I assume it is something like
    1. A = positive integers
    2. B = negative integers
    3. C = A | B
    4. C – B = A
    Which seems correct. However, I am not sure how you go from #4 to |C| > |A|. Operations like subtraction and addition on infinite sets are not well defined, AFAIK, but I don’t have as much of a math background as you all do.

  147. 147
    EricMH says:

    For instance, the size of an infinite set + 1 is still infinite. This seems to be the distinguishing characteristic between finite and infinite numbers. A finite number + 1 is a new cardinality, contrary to infinite sets.

    However, there is an approach outlined by JohnnyB that I think gets at what you are pointing out using hyper numbers.

    https://journals.blythinstitute.org/ojs/index.php/cbi/article/view/57/53

    I’m not so familiar with that approach yet, so I cannot comment.

  148. 148
    ET says:

    The value of the elements is the key to determining the cardinality.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set.

    If the cardinality was the same tat couldn’t happen, You lose.

    And seeing that I am disputing your accepted mathematics and you keep referring to them, that means you are a clueless dolt who can only repeat himself in hopes of a different outcome.

    The very definition of insanity.

    My scheme is easier to understand. And it is used throughout set theory.
    And I told why you can match them in your scheme. Are you daft?

  149. 149
    ET says:

    EricMH- there isn’t any such thing as infinity + 1. There is infinity. And then there is the density of elements in the infinite set.

  150. 150
    JVL says:

    ET: The value of the elements is the key to determining the cardinality.

    No, the cardinality has to do with the size of the sets. By definition.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set. If the cardinality was the same tat couldn’t happen, You lose.

    Then explain how I can match up the positive integers with the positive even integers one-to-one so that no element of either set is unmatched? Please explain that. I’ve asked over and over and over again.

    And seeing that I am disputing your accepted mathematics and you keep referring to them, that means you are a clueless dolt who can only repeat himself in hopes of a different outcome.

    I keep asking you questions which you do not answer. Cannot answer? I keep telling you over and over and over again how you can disprove my work. So far . . . nothing.

    The very definition of insanity.

    Then answer the one question that has been put to you over and over and over and over again: can you find an unmatched element of the positive integers or the positive even integers in my scheme? Yes or no?

    My scheme is easier to understand. And it is used throughout set theory.
    And I told why you can match them in your scheme. Are you daft?

    There is nothing wrong with my scheme. It works. It’s simple. It’s easy to understand. It’s valid. So, again:

    Can you find an unmatched element in the positive integers or the positive even integers in my scheme? Yes or no?

  151. 151
    Ed George says:

    150 comments just because someone refuses to admit that they are wrong. That is as insane as someone spending over three years defending the claim that frequency = wavelength.

  152. 152
    ET says:

    I have already explained why you can match them up under the debated and contrived scheme. What is wrong with you?

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set. If the cardinality was the same tat couldn’t happen, You lose.

    What I am saying is that proves that you are applying your methodology incorrectly. And all you do is keep repeating it as if that will change the fact highlighted above.

  153. 153
    ET says:

    No one can collect infinite elements. That means there cannot be a set of infinite elements because a set is a collection of elements.

    Jerad still has problems with facts

    So you’ve been arguing about something you don’t think exists?

    Because losers, like you, keep bringing it up. We have already been over the fact that a set with infinite elements cannot exist. The very definition of a set excludes such a thing.

    How many times do we have to do this, Jerad? How many?

  154. 154
    Jim Thibodeau says:

    Ed George, we’ll know if he really means what he says if he has written this to mathematicians or math journals to try to get it published. If he hasn’t done any of that, then no he doesn’t really believe what he says.

  155. 155
    ET says:

    EricMH @ 146: It seems correct because it is correct.

    If a set is a well defined collection of elements and we allow for sets of infinite elements, we need to consider the following as infinity is a journey:

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    It becomes a relativity issue, A relative to B at every point in time. EVERY point, into infinity- which means never ending, going on forever.

    And to determine the relative cardinality we would use the bijective function, where applicable.

    Jerad won’t accept that cuz I haven’t figured out all of the relative cardinalities. Seriously.

  156. 156
    JVL says:

    ET: I have already explained why you can match them up under the debated and contrived scheme. What is wrong with you?

    Oh good, then you agree with me.

    Obviously what you meant was that you have explained why you CAN’T match them up under my scheme but guess what, you cannot justify that with any reference or publication. My matching is valid, simple, easy to understand.

    The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. That proves there is more elements in one set. If the cardinality was the same tat couldn’t happen, You lose.

    Then, AGAIN, explain how I can match up the elements of the positive integers with the positive even integers in a one-to-one way and have no unmatched elements of either set? I’ve asked you that question over and over an over again and you keep not answering. Clearly you can’t answer it. Or won’t answer it. Which is it?

    What I am saying is that proves that you are applying your methodology incorrectly. And all you do is keep repeating it as if that will change the fact highlighted above.

    Please provide a citation which shows that my matching is incorrect. You haven’t been able to do so before even though I have asked youmany times so I’m not holding my breath.

    Let’s just call it okay? You cannot find an unmatched element of the positive integers or the positive even integers with my scheme. If you could you would have done so. You cannot provide support for your “contrived vs derived” matching issue. Clearly cardinality has nothing to do with the value of the elements of the sets involved. You have not supported your “standard” matching criteria, that doesn’t exist. You can’t find any support for saying my approach is invalid.

    I think we’re done now, yes?

  157. 157
    ET says:

    LoL! @ Acartia spearshake George. You are the moron who couldn’t grasp what I was talking about with frequency and wavelength. You had to quote-mine me and then ignore all explanations. And it was YOU and the other evoTARD minions who keep bringing it up. I shouldn’t have to keep defending it but losers like you don’t quit.

    Were you raised by humans? Just curious

  158. 158
    ET says:

    Yes, Jerad, just call it. You are just repeating yourself ad nauseum. You have nothing to add and you ignore too much.

    Good luck with that

  159. 159
    JVL says:

    ET: No one can collect infinite elements. That means there cannot be a set of infinite elements because a set is a collection of elements.

    So why are you arguing about it?

    Because losers, like you, keep bringing it up. We have already been over the fact that a set with infinite elements cannot exist. The very definition of a set excludes such a thing.

    So the set of positive integers doesn’t exist? All the mathematicians in the world will be greatly amused.

    How many times do we have to do this, Jerad? How many?

    Your call.

    Jerad won’t accept that cuz I haven’t figured out all of the relative cardinalities. Seriously.

    And you never will. Seriously..

    Time to call it quits I think. You haven’t answer questions, easy questions, which have been posed over and over and over again. You haven’t been able to back up your “contrived vs derived” criteria with documentation. You can’t point to anyone supporting your “standard” matching over anything else.

    Time to stop, yes?

  160. 160
    JVL says:

    ET: Yes, Jerad, just call it. You are just repeating yourself ad nauseum. You have nothing to add and you ignore too much.

    Answer the question: can you find an unmatched element in my matching between the positive integers and the positive even integers? Yes or no? Or run away. Your call.

  161. 161
    ET says:

    Jerad, You have ignored my responses and prattled on like a spoiled brat. If this was a formal debate they would have thrown you out for repeating the very issue that is being debated as if that settles the debate.

    Good luck being stuck in the 19th century

  162. 162
    ET says:

    Answer the question: can you find an unmatched element in my matching between the positive integers and the positive even integers?

    I not would expect to because your scheme proves they are both countable and infinite sets.

    What your scheme doesn’t do is tell us about the cardinality. For that we use the values of the elements.

    Now you answer or run away- your choice:

    Using the standard matching used for determining unions, subsets and proper subsets, can you find unmatched elements between the set of all positive integers and the set of all even positive integers?

  163. 163
    ET says:

    I not would? I would not expect to because your scheme proves they are both countable and infinite sets.

  164. 164
    ET says:

    But then again Jerad thinks people can collect infinite elements.

  165. 165
    JVL says:

    Jt: I not would expect to because your scheme proves they are both countable and infinite sets.

    Great! We know all countable infinite sets are the same size so case closed! Whew!

    What your scheme doesn’t do is tell us about the cardinality. For that we use the values of the elements.

    Cardinality has nothing to do with the values of the elements. That is just wrong.

    Now you answer or run away- your choice:

    I’m good. What I’ve been saying is easily verified by anyone doing an online search or by anyone who has taken a set theory course.

    Using the standard matching used for determining unions, subsets and proper subsets, can you find unmatched elements between the set of all positive integers and the set of all even positive integers?

    There is no “standard matching”, you made that up. And I found a matching where there were no unmatched elements. Since such a matching exists the sets have the same cardinality. Done!!

    I not would? I would not expect to because your scheme proves they are both countable and infinite sets.

    And there is a theorem which proves that all countably infinite sets have the same cardinality. Done!!

    But then again Jerad thinks people can collect infinite elements.

    Do you think the set of all integers is not infinite? Really?

    Anyway, I think we’ve cleared everything up nicely. Good. It was getting a bit long.

  166. 166
    ET says:

    JVL:

    We know all countable infinite sets are the same size so case closed!

    Only the closed-minded people who don’t grasp infinity, “know” that, Jerad.

    Using the standard matching used for determining unions, subsets and proper subsets, can you find unmatched elements between the set of all positive integers and the set of all even positive integers?

    There is no “standard matching”

    I linked to it. But thank you for proving that you are a loser and a coward. If that is how you “win” debates, then declare victory.

    Do you think the set of all integers is not infinite?

    I am saying that no one can collect infinite integers. But go ahead, do it and prove me worng.

  167. 167
    JVL says:

    ET: Only the closed-minded people who don’t grasp infinity, “know” that, Jerad.

    Nope, I showed you a theorem that says that. I guess you didn’t understand it. And you certainly did not point out a fault in the proof. So . . . done!!

    Using the standard matching used for determining unions, subsets and proper subsets, can you find unmatched elements between the set of all positive integers and the set of all even positive integers?

    Why would I use the wrong tool for the job? There’s lots of unmatched elements using your matching, there are no unmatched elements in my method. My method does the job required, your’s does not. Done! The two sets are the same size.

    I linked to it. But thank you for proving that you are a loser and a coward. If that is how you “win” debates, then declare victory.

    Uh huh. I just checked all your responses in this thread. The only things you linked to had to do with set union and proper subsets. So no, you did not provide a link to a reference regarding some “standard” matching. Stop making things up.

    I am saying that no one can collect infinite integers. But go ahead, do it and prove me worng.

    The set of positive integers is an infinite set, period. No one has to “collect” everything in a set to work with it. You really are reaching now. Even some of your links referenced infinite sets. You clearly did NOT study real set theory. You should stop saying that as it’s insulting to people who have studied it.

    There is no such thing as a “standard” matching, you made that up.

    There is no such things as a “contrived” matching, you made that up.

    You think there is no such thing as an infinite set because no one can collect an infinite number of things! Too funny.

    You say you studied set theory but you dispute some of the most basic principles so I doubt you really did take a course. What was the textbook? What was the course number? At which institution? Can you still get your money back?

    The real problem is that you don’t believe in infinity; that’s why you cannot get your head around the concept. For you infinity is just some really, really big value. But that’s not it at all. You should stop embarrassing yourself and quit arguing about things you don’t understand.

  168. 168
    ET says:

    JVL:

    Nope, I showed you a theorem that says that.

    The very theorem that is under dispute. Clearly you are a dolt.

    Why would I use the wrong tool for the job?

    That’s what you are doing.

    The only things you linked to had to do with set union and proper subsets.

    Yes, obviously you cannot read for comprehension. Try again:

    Using the standard matching used for determining unions, subsets and proper subsets, can you find unmatched elements between the set of all positive integers and the set of all even positive integers?

    I am saying that no one can collect infinite integers. But go ahead, do it and prove me wrong.

    The set of positive integers is an infinite set, period.

    And yet no one can collect infinite integers.

    You think there is no such thing as an infinite set because no one can collect an infinite number of things!

    Infinite number- LoL! – You don’t understand infinity, Jerad.

    You say you studied set theory but you dispute some of the most basic principles

    LIAR! You are a punk liar, Jerad.

    The real problem is that you don’t believe in infinity;

    More lies. It’s as if you are a loser coward.

    I made my case. Jerad either ignored it or is too stupid to understand it. Either way it is not my problem.

    Jerad, You have ignored my responses and prattled on like a spoiled brat. If this was a formal debate they would have thrown you out for repeating the very issue that is being debated as if that settles the debate.

    Good luck being stuck in the 19th century

  169. 169
    JVL says:

    ET: The very theorem that is under dispute. Clearly you are a dolt.

    You’re the only person in the whole world who is disputing it and you haven’t found a fault with the proof so, guess what, it still stands as true.

    That’s what you are doing.

    Nope, I found a matching that is one-to-one. Done.

    Yes, obviously you cannot read for comprehension. Try again:

    I didn’t see anything saying only one matching was allowed or anything about “contrived” mappings being bad.

    Using the standard matching used for determining unions, subsets and proper subsets, can you find unmatched elements between the set of all positive integers and the set of all even positive integers?

    It doesn’t matter that your “standard” matching is not one-to-one. There is no reason you cannot use whatever matching you want. And you cannot find a reference that says otherwise.

    I am saying that no one can collect infinite integers. But go ahead, do it and prove me wrong.

    Like I said, you don’t understand Set Theory.

    And yet no one can collect infinite integers.

    So what? The set of positive integers is still infinite. A “collection” does not mean someone has to go out and “collect” the items!

    LIAR! You are a punk liar, Jerad.

    Nope, I have studied set theory and I can tell you haven’t.

    I made my case. Jerad either ignored it or is too stupid to understand it. Either way it is not my problem.

    Not a problem for you if you don’t mind people thinking you don’t understand set theory.

    Jerad, You have ignored my responses and prattled on like a spoiled brat. If this was a formal debate they would have thrown you out for repeating the very issue that is being debated as if that settles the debate.

    I have responded to your responses and told you why they are incorrect and/or inconsequential. My responses are based on well-established mathematics and theorems. In a court of law I’d have volumes and volumes of work backing me up.

    If you think a theorem is wrong then you have to find a flaw in the proof. Until you find a flow in the proof it stands as being true. It’s just like the people who claim to have invented a perpetual motion machine; no one is going to believe then until they produce the goods. And you haven’t produced the goods.

    Good luck being stuck in the 19th century

    What was true in mathematics in the 19th century is still true. It’s not like physics.

    So, you still have not found a mistake in any mathematical proofs of theorems I have referenced so they still stand.

    You have failed to document your “contrived vs derived” issue so we don’t have to worry about that.

    You have failed to document your contention that only the “standard” matching is allowed so we can use whatever we like.

    You think it matters that no one can “collect” infinite integers. Now that really does make you look foolish.

  170. 170
    ET says:

    I found fault with the proof. Obviously you are just a dolt who can’t read.

    Set subtraction PROVES that there are more elements in {1,2,3,4,…} than {2,4,6,8, …}

    Your ignorance with respect to derived vs contrived isn’t an argument.

    And I am more than comfortable with the fact that no one can demonstrate that I don’t understand set theory.

    And yes a collection means the elements can be collected. Your ignorance of the English language is not an argument

    There is no reason you cannot use whatever matching you want.

    Of course there is. The reason being do you want reality or a contrivance?

    Contrived means obviously planned or FORCED. Derived means obtained from the source or origin.

    You think it matters that no one can “collect” infinite integers.

    It matters to those of us who understand English. It isn’t my fault that you are ignorant.

    I would love to debate this in a public forum that wouldn’t allow people to use what is being debated to try to settle the debate. How much of a loser coward can someone be to even try to do that? And yet that is all Jerad has done.

    But I am OK with the fact that my concept is way over Jerad’s head.

  171. 171
    ET says:

    If a set is a well defined collection of elements and we allow for sets of infinite elements, we need to consider the following as infinity is a journey:

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    It becomes a relativity issue, A relative to B at every point in time. EVERY point, into infinity- which means never ending, going on forever.

    And to determine the relative cardinality we would use the bijective function, where applicable.

    Jerad doesn’t understand infinity and Jerad doesn’t understand relativity. Jerad cannot find any fault with my example- an example of collecting. Jerad doesn’t understand that all I need is ONE scenario, like the one in this comment, to refute the claim Cantor made about countably infinite sets having the same cardinality.

  172. 172
    ET says:

    Anything that is contrived is unnatural and forced. Anything that is derived is natural. The way set unions are found is derived. The way subsets and proper subsets are found is derived. They naturally flow from the value of the elements.

  173. 173
    JVL says:

    ET: I found fault with the proof. Obviously you are just a dolt who can’t read.

    Which theorem? I referenced a few. What fault did you find? Please be specific.

    Set subtraction PROVES that there are more elements in {1,2,3,4,…} than {2,4,6,8, …}

    Only you believe so.

    Your ignorance with respect to derived vs contrived isn’t an argument.

    It is when the issue doesn’t really exist. And you cannot show that it does.

    And I am more than comfortable with the fact that no one can demonstrate that I don’t understand set theory.

    No worries there, you’re doing a good job of that yourself.

    And yes a collection means the elements can be collected. Your ignorance of the English language is not an argument

    Your ignorance of set theory and mathematics in general is pretty funny sometimes.

    Of course there is. The reason being do you want reality or a contrivance?

    You cannot prove that anyone else even uses the term “contrivance” in set theory as a negative practice. You can’t. Not surprising since you clearly never actually studied set theory.

    Contrived means obviously planned or FORCED. Derived means obtained from the source or origin.

    It’s not an issue in set theory and you cannot show that it is.

    I would love to debate this in a public forum that wouldn’t allow people to use what is being debated to try to settle the debate. How much of a loser coward can someone be to even try to do that? And yet that is all Jerad has done.

    Show the fault you found, be precise.

    But I am OK with the fact that my concept is way over Jerad’s head.

    I’ll let you know when you start making sense.

    If a set is a well defined collection of elements and we allow for sets of infinite elements, we need to consider the following as infinity is a journey:

    Do what you like but don’t expect anyone to take you seriously.

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    “for/into infinity” makes no sense. You can keep repeating if you like but you’re digging your hole deeper.

    It becomes a relativity issue, A relative to B at every point in time. EVERY point, into infinity- which means never ending, going on forever.

    “every point into infinity” makes no sense.

    And to determine the relative cardinality we would use the bijective function, where applicable.

    There is more than one bijective function, bijective means a kind of function not a particular one. Like I said, you don’t understand set theory. From Wikipedia:

    In mathematics, a bijection, bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set. There are no unpaired elements. In mathematical terms, a bijective function f: X ? Y is a one-to-one (injective) and onto (surjective) mapping of a set X to a set Y.[1][2] The term one-to-one correspondence must not be confused with one-to-one function (a.k.a. injective function)

    Jerad doesn’t understand infinity and Jerad doesn’t understand relativity. Jerad cannot find any fault with my example- an example of collecting. Jerad doesn’t understand that all I need is ONE scenario, like the one in this comment, to refute the claim Cantor made about countably infinite sets having the same cardinality.

    I’ve pointed out your mistakes over and over and over again. Now you’re just becoming a laughing stock.

    Anything that is contrived is unnatural and forced. Anything that is derived is natural. The way set unions are found is derived. The way subsets and proper subsets are found is derived. They naturally flow from the value of the elements.

    Not an issue in set theory. But since you never really studied it you wouldn’t know.

  174. 174
    JVL says:

    Also from Wikipedia:

    If X and Y are finite sets, then there exists a bijection between the two sets X and Y if and only if X and Y have the same number of elements. Indeed, in axiomatic set theory, this is taken as the definition of “same number of elements” (equinumerosity), and generalising this definition to infinite sets leads to the concept of cardinal number, a way to distinguish the various sizes of infinite sets.

  175. 175
    JVL says:

    Another bit from Wikipedia:

    For a pairing between X and Y (where Y need not be different from X) to be a bijection, four properties must hold:

    each element of X must be paired with at least one element of Y,
    no element of X may be paired with more than one element of Y,
    each element of Y must be paired with at least one element of X, and
    no element of Y may be paired with more than one element of X.
    Satisfying properties (1) and (2) means that a pairing is a function with domain X. It is more common to see properties (1) and (2) written as a single statement: Every element of X is paired with exactly one element of Y. Functions which satisfy property (3) are said to be “onto Y ” and are called surjections (or surjective functions). Functions which satisfy property (4) are said to be “one-to-one functions” and are called injections (or injective functions).[3] With this terminology, a bijection is a function which is both a surjection and an injection, or using other words, a bijection is a function which is both “one-to-one” and “onto”.[1][4]

    Gee, nothing about contrived or derived or standard. Imagine that. But not too suprising since those are not real issues.

  176. 176
    Jim Thibodeau says:

    @JVL: I had an elderly relative, now passed, who was insecure and thought as long as he never admitted he was wrong, and kept talking, then he still hadn’t lost the argument. FWIW.

  177. 177
    ET says:

    Jerad want a cracker?

  178. 178
    ET says:

    If X and Y are finite sets

    Except we are NOT discussing finite sets. Your desperation is showing

  179. 179
    ET says:

    JVL:

    “every point into infinity” makes no sense.

    Only because you don’t understand infinity. And you have issues with the English language.

  180. 180
    JVL says:

    ET: Except we are NOT discussing finite sets. Your desperation is showing

    You didn’t even read the whole quote! hahhahahahahahahahahahahahahahahahahah

    Only because you don’t understand infinity. And you have issues with the English language.

    It doesn’t make mathematical sense.

    Still no indication of the mistake you found in the proof of some theorem. I might be waiting a long time.

  181. 181
    ET says:

    Yes, your ignorance of infinity and your ignorance of the English language don’t make any sense at all.

  182. 182
    ET says:

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    Into infinity is the correct terminology. That Jerad is ignorant of that fact says it all.

  183. 183
    JVL says:

    ET: You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    At any point in time the counters will not match but “for/into infinity” does not make mathematical sense.

    Into infinity is the correct terminology. That Jerad is ignorant of that fact says it all.

    Nope, it is not. Show me a math textbook that uses it.

    Still no indication of which proof of some theorem you found a mistake in. Strange, you seemed so sure . . .

  184. 184
    ET says:

    JVL:

    At any point in time the counters will not match but “for/into infinity” does not make mathematical sense.

    That is only because YOU are ignorant of the concept.

    Into infinity is the correct terminology. That Jerad is ignorant of that fact says it all.

    Nope, it is not.

    Yes, it is. Anyone can use google to find out that what I said is correct. Here are some examples: https://www.wordhippo.com/what-is/sentences-with-the-word/infinity.html

  185. 185
    ET says:

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    After the first second, there will NEVER be a time when the two counters are equal. That proves the number of elements are not the same.

  186. 186
    ET says:

    ” The pool is so designed that its end wall is on a level with the backwaters, conveying the illusion of stretching into infinity.”

    Theoretically, a line can extend into infinity.

    The view tapers off into infinity. That one is from merriam-webster

  187. 187
    Jim Thibodeau says:

    One definition of infinity is “the amount of time we will be waiting before any mathematician, anywhere in the multiverse, agrees with ET.”

  188. 188
    ET says:

    One definition of infinity is “the amount of time we will be waiting before any mathematician, anywhere in the multiverse, can refute ET.” Also “the amount of time we will be waiting before any mathematician, anywhere in the multiverse, can find a use for claiming all countably infinite sets have the same cardinality.”

    Look, Jim, my example of the two counters represents the real world. And in the real world Cantor’s conjecture fails.. That leads to definition 3: “the amount of time we will be waiting before any mathematician, anywhere in the multiverse, can show that the two counters will ever be the same after the first count.”

  189. 189
    JVL says:

    ET

    Let’s check out the specifically mathmatical statements in your linked document:

    Bolzano’s theories of mathematical infinity anticipated Georg Cantor’s theory of infinite sets.

    No problem there, nothing about “into” infinity.

    But this spectrum is at right angles to the first, generating a person-space with an infinity of different potential placements.

    Not sure about what’s being discussed her but the word infinity is being used to refer to the ‘number’ of options.

    As time tends to infinity both the variance and the total number tends to zero.

    “Tends to” is not at all the same as “into”, in this case they are just saying that time is getting larger and larger. It’s a limit argument which has a definite mathematical meaning.

    This work contains fundamental ideas of projective geometry such as the cross-ratio, perspective, involution and the circular points at infinity.

    Ah, now that one is quite a bit more complicated but again they are not saying “into”. Personally I would not say “at” infinity either but I’d have to seen the whole source before I came down hard on that one.

    Euler asserts that the sum of the harmonic series equals the natural logarithm of infinity plus a quantity that is nearly a constant.

    I’m not sure that is even correct but it would take some time to research but, again, no one is saying “into” infinity. The natural logarithm of infinity . . . weird.

    I will admit that frequently, especially when speaking, mathematicians will use terms that they would not use in a paper or textbook but as long as no one is being nit-picky no one cares much.

    The rest are all from other fields or literature and so their uses are not pertinent. In mathematics words mean what you say they mean. For example . . .

    In graph theory (invented by Euler by the way) a “tree” is a particular kind of graph or part of a graph. A “path” also has a very specific meaning and only that meaning. In graph theory. In other parts of mathematics they may have different meanings. You get used to it if you study a lot of mathematics.

    After the first second, there will NEVER be a time when the two counters are equal. That proves the number of elements are not the same.

    “A time” means something finite and we’re talking about something infinite. I’ve told you this over and over and over again.

    Theoretically, a line can extend into infinity.

    I’d say “a line can extend infinitely far” myself but I might let that one go because the mathematics is clear.

    The view tapers off into infinity. That one is from merriam-webster

    Like I said, math doesn’t care about general usage.

  190. 190
    JVL says:

    `Et: Look, Jim, my example of the two counters represents the real world. And in the real world Cantor’s conjecture fails..

    But we’re talking about mathematics!! hahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahah

    And it’s not a conjecture!

  191. 191
    ET says:

    JVL:

    I’d say “a line can extend infinitely far” myself…

    And you sound like an imbecile.

    “A time” means something finite and we’re talking about something infinite.

    EVERY time- FOREVER. As I said, you clearly don’t understand infinity.

    But we’re talking about mathematics!!

    Wow. My example is represents the real world of set theory.

    Fields of literature are pertinent. Mathematics is full of definitions. Definitions are the meanings of the words being used. If you don’t understand the words used in the mathematical definitions then you are lost, like you are now.

  192. 192
    ET says:

    Proving JVL is lame:

    Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    NOTE: ALWAYS and FOREVER. That is then followed by , i.e. for/ into infinity. So what does Jerad do? Pick on the “into infinity”, which, as it turns out, is perfectly fine terminology.

    Counter A will ALWAYS and FOREVER have a higher count than counter B.

    Now what, Jerad?

  193. 193
    JVL says:

    ET: EVERY time- FOREVER. As I said, you clearly don’t understand infinity.

    “Every time” means a moment, a certain point. That’s finite.

    Wow. My example is represents the real world of set theory.

    But it doesn’t represent the mathematics of set theory.

    Fields of literature are pertinent. Mathematics is full of definitions. Definitions are the meanings of the words being used. If you don’t understand the words used in the mathematical definitions then you are lost, like you are now.

    Mathematicians are very clear in defining their use of terms so things are clear. As someone who claims to have studied mathematics you should know that.

    NOTE: ALWAYS and FOREVER. That is then followed by , i.e. for/ into infinity. So what does Jerad do? Pick on the “into infinity”, which, as it turns out, is perfectly fine terminology.

    Whatever. I’ll drop it.

    Counter A will ALWAYS and FOREVER have a higher count than counter B.

    At any given moment of time that is true. But a moment of time is at some finite point. You cannot be at infinite with a clock.

    Now what, Jerad?

    You haven’t established that your “contrived vs derived” criteria is real. You could work on that.

    You haven’t established that your “standard” matching criteria is real, i.e. there is no reason to prefer your matching when trying to establish cardinality. You could work on that.

    You haven’t specified which theorem you found fault with or what fault you found. You could work on that. There are lots of theorems involved so you need to be specific.

    You haven’t found an unmatched element in my matching scheme. There are lots of unmatched elements in your matching scheme but that’s not the point since your scheme is not “better” than mine. And if you think it matters more then you need to document your reasons for that with references. You could work on those things as well.

  194. 194
    ET says:

    JVL:

    “Every time” means a moment, a certain point. That’s finite.

    LoL! EVERY means forever. Forever is infinity.

    Mathematicians are very clear in defining their use of terms so things are clear.

    I know that. YOU are the one having difficulty with definitions.
    Counter A will ALWAYS and FOREVER have a higher count than counter B.

    At any given moment of time that is true.

    EVERY moment, throughout time- meaning for infinity.

    You haven’t established that your “contrived vs derived” criteria is real.

    It’s called parsimony.

    You haven’t established that your “standard” matching criteria is real

    Of course I have. Your quote-mining means nothing to me. I know what I said. You have difficulties with comprehending what is written.

    I provided a real world example. Either Cantor’s conjecture works in the real world, obviously it doesn’t, or it should be rethought.

    And AGAIN, that you use the very thing being debated to try to win the debate just proves that you are a dolt. Good luck with that.

  195. 195
    ET says:

    Counter A will ALWAYS and FOREVER have a higher count than counter B.

    ALWAYS and FOREVER, which means for infinity.

  196. 196
    JVL says:

    ET: LoL! EVERY means forever. Forever is infinity.

    But it’s not infinity. Infinity is not a moment, you don’t cross over “into” infinity.

    I know that. YOU are the one having difficulty with definitions.
    Counter A will ALWAYS and FOREVER have a higher count than counter B.

    Enjoy being at odds with every mathematician on the planet.

    EVERY moment, throughout time- meaning for infinity.

    Whatever.

    It’s called parsimony.

    No, your “contrived vs derived” issue has nothing to do with parsimony. You made it up. I know you made it up since you cannot back it up with references.

    Of course I have. Your quote-mining means nothing to me. I know what I said. You have difficulties with comprehending what is written.

    Good luck being at odds with every mathematician on the planet. Where is that theorem whose proof you found fault with by the way?

    I provided a real world example. Either Cantor’s conjecture works in the real world, obviously it doesn’t, or it should be rethought.

    Nothing to do with mathematics. And you said you studied set theory. That was clearly false as everyone can now see.

    And AGAIN, that you use the very thing being debated to try to win the debate just proves that you are a dolt. Good luck with that.

    When you are maybe the only person on the planet who is doubting well-established and accepted mathematics then it’s up to you to DO SOME WORK and prove your case. So far you just keep repeating what you’ve already said . . . in hopes I’ll give up and concede the battleground?

    ALWAYS and FOREVER, which means for infinity.

    Nope, that’s how I know you never actually studied set theory.

    So, let’s recap . . .

    You have yet to provide any kind of support for your “contrived vs derived” criteria. I claim you made it up. Can you prove me wrong?

    You have yet to provide any kind of support your your “standard matching” criteria. Again, I think you made that up. You haven’t been able to provide anything in support so I’m not holding my breath that you will.

    You have not provided any details about which theorem you found fault with or what that fault was. Perhaps it’s best just to assume you won’t be able to do that and chalk that up for a “loss” for your side.

  197. 197
    ET says:

    JVL:

    But it’s not infinity.

    Forever is infinity.

    Enjoy being at odds with every mathematician on the planet.

    I am comforted by the fact they cannot refute what I say. They can only spout gibberish, like you ae doing.

    Nothing to do with mathematics.

    Of course it does.

    When you are maybe the only person on the planet who is doubting well-established and accepted mathematics then it’s up to you to DO SOME WORK and prove your case.

    I proved my case.

    No, your “contrived vs derived” issue has nothing to do with parsimony.

    It has everything to do with parsimony. You are adding on to what naturally exists. You are inventing something out of nothing.

    ALWAYS and FOREVER, which means for infinity.

    Nope, that’s how I know you never actually studied set theory.

    LoL! So because you are an ignorant ass it means something about me? Really?

    You have yet to provide any kind of support your your “standard matching” criteria.

    Liar

    So to recap- all Jerad can do is lie, act like an ignoramus and spew false accusations. Oh, and use the very thing being debated to try to settle the debate.

    You’re a punk, Jerad.

  198. 198
    ET says:

    My real world example proves there is a problem with Cantor’s thinking about the cardinality of countably infinite sets. Jerad can’t handle that and throws a hissy-fit.

  199. 199
    Jim Thibodeau says:

    Is nobody here going to support ET?

    Nobody?

  200. 200
    Ed George says:

    J T

    Is nobody here going to support ET?

    Nobody?

    I was going to wait until this thread had 200 comments.

  201. 201
    kairosfocus says:

    It seems there is need here to contrast potential and actual infinite. A counter going 123 vs 246 will read differently at any given time but both in principle can increment countably and without any finite upper bound. Cardinality is thus speaking of a qualitatively different thing here. Countable transfinite.

  202. 202
    JVL says:

    ET: Forever is infinity.

    Oh dear, you really do not understand set theory.

    I am comforted by the fact they cannot refute what I say. They can only spout gibberish, like you ae doing.

    I guess that’s why you are not teaching mathematics, doing mathematical research, writing about mathematics or even applying any mathematics above arithmetic.

    I proved my case.

    Far, far, far from it. You could not link to any mathematical reference that agreed with your “contrived vs derived” stance. You could not support your “standard matching” statement. And you have yet to specify which theorem you are disputing and what fault you found with its proof. You have to make specific mathematical statements not just apply to dictionaries or common usage of terms.

    it has everything to do with parsimony. You are adding on to what naturally exists. You are inventing something out of nothing.

    So? My matching meets the definition (listed above) so it’s valid. You really don’t understand mathematics at all.

    ALWAYS and FOREVER, which means for infinity.

    Sigh.

    LoL! So because you are an ignorant ass it means something about me? Really?

    Which set theory books have you read? Which course did you take? At which university? What textbook was used?

    So to recap- all Jerad can do is lie, act like an ignoramus and spew false accusations. Oh, and use the very thing being debated to try to settle the debate.

    You are disputing something, no one else. It’s down to you to point out specific mathematical faults in a proof of a theorem which you cannot do. So, there is no debate because the theorem’s proof stands which means the theorem is true.

    You’re a punk, Jerad.

    One who knows how set theory works.

    My real world example proves there is a problem with Cantor’s thinking about the cardinality of countably infinite sets. Jerad can’t handle that and throws a hissy-fit.

    You call that finding fault with a theorem? Cantor was not trying to solve a real-world problem!! He was dealing with abstract mathematical structures. Thank you for confirming, once again, that you do not understand set theory. Cantor’s work stands, there is no debate. There’s just you not wanting to admit you don’t know what you’re talking about.

  203. 203
    ET says:

    JVL:

    Oh dear, you really do not understand set theory.

    Non-sequitur.

    I proved my case.

    Far, far, far from it.

    YOU don’t get to say. YOU can’t even think for yourself. YOU shit yourself when trying to respond to my case.

    ALWAYS and FOREVER, which means for infinity.

    Sigh.

    Yes, your ignorance is becoming legendary.

    You are disputing something, no one else.

    So what? It’s still moronic to use the very thing that is being debated to try to settle the debate. You have to be a total ignoramus to try something like that.

    My real world example proves there is a problem with Cantor’s thinking about the cardinality of countably infinite sets. Jerad can’t handle that and throws a hissy-fit.

    Mathematics is used in the real world. The real world is how we test the mathematics to see if it stands up to real scrutiny.

    Clearly you don’t know what you are talking about. You are a sad and pathetic little nobody.

  204. 204
    ET says:

    Jimbo:

    Is nobody here going to support ET?

    No one here can refute what I have said. No one. And I am more than OK with that.

    Jerad can’t even read. And I know that Acartia Eddie has reading comprehension issues. And you have proven to be an incompetent dolt.

  205. 205
    ET says:

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    After the first second, there will NEVER be a time when the two counters are equal. That proves the number of elements are not the same.

    Jerad can’t handle the truth. Jerad can’t even read.

  206. 206
    JVL says:

    ET: YOU don’t get to say. YOU can’t even think for yourself. YOU shit yourself when trying to respond to my case.

    Hardly. I did get a bit bored though, telling you over and over and over again where you are mistaken.

    So what? It’s still moronic to use the very thing that is being debated to try to settle the debate. You have to be a total ignoramus to try something like that.

    It can only be said to be under debate if you can find a mistake which you clearly cannot do.

    My real world example proves there is a problem with Cantor’s thinking about the cardinality of countably infinite sets. Jerad can’t handle that and throws a hissy-fit.

    Real-world examples don’t matter in proving mathematical theorems. See, you don’t understand how it works.

    Mathematics is used in the real world. The real world is how we test the mathematics to see if it stands up to real scrutiny.

    The real world is used to test mathematical models and applications but not theorems. You really don’t get it.

    Clearly you don’t know what you are talking about. You are a sad and pathetic little nobody.

    Someone who can keep track of all the claims you’ve made that you haven’t supported.

    Jerad can’t even read. And I know that Acartia Eddie has reading comprehension issues. And you have proven to be an incompetent dolt.

    You didn’t even read a whole passage I quoted above!

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    Is there an echo in here?

    After the first second, there will NEVER be a time when the two counters are equal. That proves the number of elements are not the same.

    Nope, Cantor proved you’re wrong and you cannot find a mistake in his work.

    Jerad can’t handle the truth. Jerad can’t even read.

    I know the mathematics, you don’t. You shouldn’t be arguing about things you don’t understand.

  207. 207
    ET says:

    You don’t know how to think, Jerad. You don’t know the mathematics. You can’t even read for comprehension.

    Cantor didn’t prove I am wrong. Cantor didn’t know about relativity.

    A real world example proved that Cantor was wrong. And you have nothing to say because all you can do is parrot what is being debated.

    As I said, I will gladly take this to a public forum and make sure that you can’t use the thing being debated for support. I will hammer the moderators with that fact. I will prove that you can’t handle basic set subtraction. And I will easily prove that you cannot grasp infinity.

    You can’t demonstrate that I am wrong. You cannot find a real fault with my example.

    You are a pathetic little whiny nobody

  208. 208
    ET says:

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    After the first second, there will NEVER be a time when the two counters are equal. That proves the number of elements are not the same.

    Jerad refuses to answer the questions. Jerad is an ignorant coward who clearly doesn’t understand the mathematics involved.

  209. 209
    JVL says:

    ET: You don’t know how to think, Jerad. You don’t know the mathematics. You can’t even read for comprehension.

    At least I can understand the proof of a theorem.

    Cantor didn’t prove I am wrong. Cantor didn’t know about relativity.

    Relativity has nothing to do with the cardinality of infinite sets.

    A real world example proved that Cantor was wrong. And you have nothing to say because all you can do is parrot what is being debated.

    The real world is not an issue when discussing pure mathematics.

    As I said, I will gladly take this to a public forum and make sure that you can’t use the thing being debated for support. I will hammer the moderators with that fact. I will prove that you can’t handle basic set subtraction. And I will easily prove that you cannot grasp infinity.

    It would be a short debate; I’d go over the proofs of the theorems and when you couldn’t find a mathematical mistake it’d be over.

    You can’t demonstrate that I am wrong. You cannot find a real fault with my example.

    In order to check your counters you have to pick a particular moment to do that. That’s a finite value. That’s not inifinity.

    You are a pathetic little whiny nobody

    At least I understand set theory.

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    There is an echo in here! Or someone thinks if they repeat something often enough in bold type everyone else will give up or agree with them.

    After the first second, there will NEVER be a time when the two counters are equal. That proves the number of elements are not the same.

    Nope because you can’t check at infinity ’cause you never get there.

    Jerad refuses to answer the questions. Jerad is an ignorant coward who clearly doesn’t understand the mathematics involved.

    I did answer your questions; I admitted that at any give time one counter would be twice the other. But that’s not at infinity ’cause you’ll never get there.

  210. 210
    ET says:

    Jerad, please go have your diaper changed.

    I admitted that at any give time one counter would be twice the other. But that’s not at infinity ’cause you’ll never get there.

    There isn’t any “there” to get to. If, at every point in time (meaning for infinity), one counter will always (meaning for infinity) have a higher count than the other, then the cardinality will never be the same.

    There isn’t any checking at infinity because that is nonsense. The counters are checked for infinity. That means they are checked every second for infinity. And for infinity one counter will always have a higher count, ie more elements and therefore a greater cardinality.

    Relativity has everything to do with infinity. How many times do I have to tell you that?

  211. 211
    ET says:

    As I said, I will gladly take this to a public forum and make sure that you can’t use the thing being debated for support. I will hammer the moderators with that fact. I will prove that you can’t handle basic set subtraction. And I will easily prove that you cannot grasp infinity.

    It would be a short debate; I’d go over the proofs of the theorems and when you couldn’t find a mathematical mistake it’d be over.

    So you would use the very thing being debated to settle the debate? Right after I made sure the moderators agreed to disallow it? Really?

    I would bring out my example and prove that A) you can’t comprehend what you read and B) you don’t understand infinity. And then it would be over.

  212. 212
    JVL says:

    ET: Jerad, please go have your diaper changed.

    I’m not the one saying stuff that isn’t true.

    There isn’t any “there” to get to. If, at every point in time (meaning for infinity), one counter will always (meaning for infinity) have a higher count than the other, then the cardinality will never be the same.

    Cantor figured out how to deal with that. You don’t understand his ideas. That’s clear.

    There isn’t any checking at infinity because that is nonsense. The counters are checked for infinity. That means they are checked every second for infinity. And for infinity one counter will always have a higher count, ie more elements and therefore a greater cardinality.

    The set of positive even integers has the same cardinality as that of the positive integers. I showed you a proof, you couldn’t find fault with it. There is no debate unless you can find a mistake.

    Relativity has everything to do with infinity. How many times do I have to tell you that?

    You can say it as often as you like that doesn’t make it true. Why don’t you find a reference that back that up?

    As I said, I will gladly take this to a public forum and make sure that you can’t use the thing being debated for support. I will hammer the moderators with that fact. I will prove that you can’t handle basic set subtraction. And I will easily prove that you cannot grasp infinity.

    If the moderators were mathematicians they would laugh you out of the building. You know this because you know no one supports your view. If you want to debate a theorem then you have to find fault with its proof, something you haven’t been able to do. You’re just saying the same wrong stuff over and over and over again.

    So you would use the very thing being debated to settle the debate? Right after I made sure the moderators agreed to disallow it? Really?

    I would show them the proof of the theorem. After they accepted that it would be up to you to find a mistake. I wouldn’t USE the theorem, I’d prove it.

    I would bring out my example and prove that A) you can’t comprehend what you read and B) you don’t understand infinity. And then it would be over.

    Again, they would laugh you out of the building.

    Debating a theorem means disproving it. You haven’t done that. Do you even understand what a proof is? This is not like physics or biology or any other science. Only mathematics has theorems, everyone else has theories and they are NOT at all the same thing.

    You really, really do not understand how mathematics works.

  213. 213
    ET says:

    No, Cantor did NOT figure out a way to deal with my example. You are obviously content to keep misrepresenting reality.

    I found the mistake. Cantor’s conjecture doesn’t match reality. When Einstein formulated his model it wasn’t widely accepted until after the real world proved it to be true.

    And no, they would laugh YOU out of the building. Your low double-digit IQ just cannot handle new ideas.

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    After the first second, there will NEVER be a time when the two counters are equal. That proves the number of elements are not the same.

    eat that.

  214. 214
    ET says:

    The set of positive even integers has the same cardinality as that of the positive integers.

    Only if you ignore reality. Which is what you always do.

  215. 215
    JVL says:

    ET: No, Cantor did NOT figure out a way to deal with my example. You are obviously content to keep misrepresenting reality.

    AGAIN, Cantor was trying to solve a problem in abstract mathematics. I guess you just can’t grasp that and have to try and force everything back to stuff you know. Good luck with that.

    I found the mistake. Cantor’s conjecture doesn’t match reality. When Einstein formulated his model it wasn’t widely accepted until after the real world proved it to be true.

    Einstein was trying to model the real world, Cantor wasn’t. You keep making this mistake over and over and over again. But, then again, you really don’t understand mathematics.

    I would bring out my example and prove that A) you can’t comprehend what you read and B) you don’t understand infinity. And then it would be over.

    If you can’t find a fault with the proof of a theorem the “dispute” is over.

    Again, they would laugh you out of the building.

    No mathematician in the world would laugh at what I am saying.

    You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B?

    After the first second, there will NEVER be a time when the two counters are equal. That proves the number of elements are not the same.

    eat that.

    Hmm . . .it looks a bit rancid to me; I’ll pass.

    Only if you ignore reality. Which is what you always do.

    How many times can you NOT understand that some mathematics is purely abstract and has no requirement to model reality? Whatever. You still haven’t found a mathematical error in any proof of any theorem so there is no dispute. Just you not wanting to admit you got it wrong. Which everyone can see.

    Have you asked yourself: why is no one else from UD defending you one this matter? Why is that? Could it be because they don’t want to support something that is clearly and obviously false? You should think about that.

  216. 216
    ET says:

    The fault with the proof is that you are conflating two different things. That you can find a one to one correspondence doesn’t necessarily mean the cardinality is the same.

    The real world is the tell. I found something in the real world that contradicts Cantor’s claim that all countably infinite sets have the same cardinality. You cannot deal with it and can only keep referring to the very thing I am disputing. And it doesn’t matter that I am the only one disputing it. The fact remains is that you cannot use the very thing being disputed in order to settle the dispute.

    That you cannot grasp that simple fact proves that you are a simpleton.

    Have you asked yourself: Why do you keep doing that and think it means something? You should think about that- if you had the ability to think for yourself.

  217. 217
    ET says:

    If a real world example contradicts an abstract thought, the abstract thought is wrong. Pure and simple. And I have provided a real world example that contradicts Cantor’s abstract thought.

  218. 218
    JVL says:

    ET: The fault with the proof is that you are conflating two different things. That you can find a one to one correspondence doesn’t necessarily mean the cardinality is the same.

    Well clearly you haven’t even read the proof or understood it. Seriously, you think you can just make stuff up and expect people to believe you? That is the whole point of the proof!!

    The real world is the tell. I found something in the real world that contradicts Cantor’s claim that all countably infinite sets have the same cardinality. You cannot deal with it and can only keep referring to the very thing I am disputing. And it doesn’t matter that I am the only one disputing it. The fact remains is that you cannot use the very thing being disputed in order to settle the dispute.

    The mathematics does not reference the real world at all. It’s not an issue. You keep bringing it up and everyone knows that what you say is not the case. There is a theorem which has a proof. If you want to dispute it, that’s fine. But no one is going to consider your dispute worthwhile unless you can find a valid mathematical mistake. Not just making stuff up you hope sticks, find something that is actually wrong. But, you’d have to actually understand the mathematics to do that.

    That you cannot grasp that simple fact proves that you are a simpleton.

    I grasp that you, actually, are just making stuff up and hoping that I stop arguing with you in which case you can then claim victory. You clearly do not understand even what a proof entails.

    Have you asked yourself: Why do you keep doing that and think it means something? You should think about that- if you had the ability to think for yourself.

    I think it’s important that people who make weird and false claims about known and established mathematical facts are called on that publicly. I think it worth showing other readers where the fault is and what the truth actually is. You, clearly, don’t really care about the actually mathematics being discussed; you just want to win an argument and you keep making up stuff to try and get me to go away. But if you really understood the mathematics you wouldn’t need to keep changing your tactics.

    You don’t understand the math. You’ve never actually taken a proper (as in 300-level or above) set theory course. You’ve never been able to back up your claim about “contrived vs derived” matchings (which you have dropped because it wasn’t working and you got called on it). You’ve stopped insisting on there being a “standard” matching again because you weren’t able to back it up and got called on in. And now you claim the theorem (which you can’t even name) is conflating one-to-one correspondence and cardinality when that is the whole point of the proof! It’s been proved! Find a mistake or stop trying to argue about stuff you very clearly do not understand.

  219. 219
    JVL says:

    ET: If a real world example contradicts an abstract thought, the abstract thought is wrong. Pure and simple. And I have provided a real world example that contradicts Cantor’s abstract thought.

    Now you’ve made it completely clear: you know zilch about mathematics. Thanks. You shot yourself in the foot so well I don’t have to make that point ever again.

    Incredible.

  220. 220
    ET says:

    JVL:

    Well clearly you haven’t even read the proof or understood it.

    That isn’t an argument. And you could never support that claim.

    The mathematics does not reference the real world at all.

    Stop saying shit that has nothing to do with what you are responding to.

    And I don’t care about you. You aren’t anyone so claiming victory over a nobody is very meaningless.

    I backed up my claims with respect to the standard matching. I gave the CONTEXT and you ignored it. My tactics haven’t changed. As I said, you can’t read and you cannot follow along. Sad, really.

    There isn’t anything established about the claim that all countably infinite sets have the same cardinality. Being the consensus thought of people stuck in the 19th century is also meaningless. Those same people can’ even figure out how to use the concept or if it is of any use at all.

    So stuff it with your “established” BS.

    Now you’ve made it completely clear: you know zilch about mathematics.

    That’s also not an argument. It’s just the opinion of someone who can’t read.

  221. 221
    ET says:

    This is what Jerad linked to as the proof we are discussing: Countable set

    I AGREE with the definition provided. I have always made that very clear. So obviously I have read it. I have even discussed bijective functions with Jerad. So obviously I understand it.

    All I am saying is that the definition does not lead to the conclusion that the cardinalities are also the same. THAT is what Cantor, et al., can’t wrap their little minds around- Yes to bijection and No to equal cardinalities. That is the real mystery of infinity.

    But then again, Jerad has been too stupid to grasp that fact for years. I am sure that I will get attacked for not knowing mathematics. And that is to be expected from little minds when they encounter something new.

  222. 222
    Jim Thibodeau says:

    @JVL if you really want to cause ET to have issues, bring up the Riemann Rearrangement Theorem. He might have a cerebral event. 🙂

  223. 223
    JVL says:

    ET: Stop saying shit that has nothing to do with what you are responding to.

    You’re right, I should have realised that, according to you, if you can’t see something in the real world then it must be false. A completely unmathematical view. But it’s yours.

    I backed up my claims with respect to the standard matching. I gave the CONTEXT and you ignored it. My tactics haven’t changed. As I said, you can’t read and you cannot follow along. Sad, really.

    You did not provide a specific statement in a mathematical discussion that said your “standard” matching is preferred. You just assumed that. But it’s not true. That Wikipedia article linked to, in fact,, uses my matching to show that the set of all positive even integers has the same cardinality as the positive integers. Thanks.

    There isn’t anything established about the claim that all countably infinite sets have the same cardinality. Being the consensus thought of people stuck in the 19th century is also meaningless. Those same people can’ even figure out how to use the concept or if it is of any use at all.

    Okay, you explain how I can demonstrate a way to match up two infinite sets, one-for-one, with no element of either set without a unique partner in the other set and NOT have the sets be the same size. You’d have to find an unmatched element with the matching being used. You cannot insist on your “standard” matching, you have to work with what is presented. And that is something you have never, ever been able to do. That’s the nub of the whole matter. You cannot break the matching I used and is used in the Wikipedia article. You can’t break it so it stands.

    So stuff it with your “established” BS.

    It’s established because it works mathematically.

    All I am saying is that the definition does not lead to the conclusion that the cardinalities are also the same. THAT is what Cantor, et al., can’t wrap their little minds around- Yes to bijection and No to equal cardinalities. That is the real mystery of infinity.

    It’s clear you don’t understand the concepts at all. AGAIN, explain how you can match up two sets, one-to-one, with no element of either set without a unique partner in the other set and yet still think they are not the same size. You have never, ever been able to break the matching I used which is also used in the Wikipedia article. That’s why you started falling back on non-issues like “contrived” or “standard” matching. Those are NOT real criteria. You WANT them to be criteria because you can’t break the used matching.

    But then again, Jerad has been too stupid to grasp that fact for years. I am sure that I will get attacked for not knowing mathematics. And that is to be expected from little minds when they encounter something new.

    It’s not new, I hear it all the time from people who can’t break out of their “real world” box and think outside of it.

    Break the matching presented or admit you can’t. That’s it. No “contrived” argument without a specific mathematic support. No “standard” argument without a specific mathematic support. Break it or admit you’re wrong.

  224. 224
    JVL says:

    Jim Thibodeau: if you really want to cause ET to have issues, bring up the Riemann Rearrangement Theorem. He might have a cerebral event. ????

    ET only works with things he can experience in the real world. I wonder how that affects his theology?

  225. 225
    ET says:

    I have already explained why there is a one to on e correspondence. Are you really that stupid?

    It is the nature of countably infinite sets. As I said, your small, limited min just cannot grasp new concepts.

    Jerad thinks that people making shot up = abstract math, which = them being a genius.

  226. 226
    ET says:

    JVL:

    ET only works with things he can experience in the real world.

    JVL thinks that making shit up means it works.

    And I don’t have any theology. I am an IDist because the real world demonstrates that ID is the only viable scientific possibility

  227. 227
    ET says:

    And if I really want to cause issues with JVL, Jimbo, bob o’h, seversky and Acartia Eddie, all I have to do is present the evidence for ID.

    It’s always very telling that they avoid such discussions.

  228. 228
    ET says:

    JVL:

    It’s established because it works mathematically.

    If it worked mathematically then set subtraction wouldn’t contradict it. My example wouldn’t contradict it. And yet both contradict it.

    And YOU haven’t been able to explain that with anything but your ignorant spewage.

  229. 229
    ET says:

    @ Jim Thibodeau, loser” Please explain, if you can, why I would have an issue with Riemann series theorem.

    Or is spewing cowardly innuendoes really the best that you can do?

  230. 230
    JVL says:

    ET: I have already explained why there is a one to on e correspondence. Are you really that stupid?

    That means no unmatched elements does it not?

    It is the nature of countably infinite sets. As I said, your small, limited min just cannot grasp new concepts.

    What does that mean: it is the nature of infinite sets? That you can match them up so every element has a partner but one set is still bigger? How does that work then?

    Jerad thinks that people making shot up = abstract math, which = them being a genius.

    No, they have to PROVE their work. You said you studied set theory so you should know that.

    JVL thinks that making shit up means it works.

    No, it has to be proved.

    It’s always very telling that they avoid such discussions.

    I’ve learned to stick to the mathematics.

    If it worked mathematically then set subtraction wouldn’t contradict it. My example wouldn’t contradict it. And yet both contradict it.

    Your set subtraction does not work for very many examples. One-to-one matching works for everything so it’s the superior method.

    Consider the two sets: S = the positive multiples of 7 and P = the positive prime numbers.

    Which set has a larger cardinality according to your method?

    Or consider the set of rational numbers. I assume you’d say it has a larger cardinality that the positive integers but how much larger? What is its “relative” cardinality.

    How about the set of all algebraic functions? Compare them to the transcendental functions. How does “set subtraction” help you there?

    When you have one method which works for example after example after example and one that only “works” for a very few cases you throw out the one that barely “works”. Set subtraction isn’t used because it doesn’t really work. “Relative cardinalities” aren’t used because they aren’t true AND they don’t work.

    And YOU haven’t been able to explain that with anything but your ignorant spewage.

    I’ve asked you over and over and over again how, under my mapping and the one used in the Wikipedia article, that there are no unmatched elements in the example we are generally referring to. You have never, ever been able to point to even one unmatched element. So, explain to me how that can happen and yet one set be larger. And no weasel words like “it’s the nature of countably infinite sets” which is not an explanation. That just a way of saying “I don’t know”. How can you have NO unmatched elements and still have the sets be different sizes? Explain that.

  231. 231
    ET says:

    Jerad, Please learn how to read.

    Your set subtraction does not work for very many examples.

    Nonsense.

    Stay focused on what we are discussing. Stop trying to change it. I have already explained how my method works with the sets you are spewing. Obviously you have issues.

    How does it work that there is the same cardinality and yet I have examples that contradict that? How does that work? By ignoring it? You are a loser, Jerad.

    And no weasel words like “it’s the nature of countably infinite sets” which is not an explanation.

    As I said, your little mind cannot grasp what I am saying.

    Set subtraction works. It is used. Relative cardinalities work because they are true. And the bijective functions prove that it works.

    It’s as if you are a just a willfully ignorant troll

  232. 232
    ET says:

    And again, no one is matching the elements. You are matching their position in the set. That’s it.

    Basic set arithmetic is a thorn in your concept. And all you can do is hand-wave it away.

  233. 233
    ET says:

    Jerad sez that set subtraction doesn’t work with infinite sets. The problem is Jerad is a nobody and doesn’t get to make that decision. If there wasn’t any unmatched elements set subtraction would show that. And yet it shows the opposite.

    So it is clear that there are unmatched elements and no unmatched positions. Jerad cannot understand that.

  234. 234
    JVL says:

    ET: Nonsense. Stay focused on what we are discussing. Stop trying to change it. I have already explained how my method works with the sets you are spewing. Obviously you have issues.

    Explain how it works with the positive multiples of 7 compared to the positive prime numbers.

    How does it work that there is the same cardinality and yet I have examples that contradict that? How does that work? By ignoring it? You are a loser, Jerad.

    Set subtraction is the wrong way to deal with the size of the sets! So it doesn’t work when establishing cardinality. Your set subtraction is taking out some elements. But, guess what? There are still infinitely many numbers left!! Not infinity divided by two. How can that work? I guess we have to thing outside of your reality box.

    As I said, your little mind cannot grasp what I am saying.

    You are NOT explaining how there can be a one-to-one matching and yet one set is still larger. You have completely failed to explain how that works. Shouldn’t there be unmatched elements if one set is bigger? Where are they?

    Set subtraction works. It is used. Relative cardinalities work because they are true. And the bijective functions prove that it works.

    No, One-to-one matchings prove that sets are the same size otherwise there’d be unmatched elements. Can you find any unmatched elements? Yes or no?

    It’s as if you are a just a willfully ignorant troll

    I’m asking you a particular question based on your claims and your methods: IF the set of positive integers is larger than the set of positive even integers then under the matching I proposed (and the one used in the Wikipedia article) there should be unmatched elements in the set of positive integers. If you can’t find an unmatched element then the sets must have the same number of elements. So, can you find an unmatched element? Answer that question.

    And again, no one is matching the elements. You are matching their position in the set. That’s it.

    That’s fair. There is no rule that says I can’t do that. It’s used in the Wikipedia article. You’ll see it used over and over and over again.

    If I had a basket of apples and a basket of oranges could you not use the same matching technique to see which basket had more fruits? Yes, you could. The “value” of the elements is NOT the point. The only thing we’re talking about is how many elements there are. That’s it. So take an element from set one and partner it with an element from set two. Keep going until one set runs out of elements. If the other set still has elements unmatched then it’s bigger. Simple.

    So, again: can you find an unmatched element? Yes or no?

    Basic set arithmetic is a thorn in your concept. And all you can do is hand-wave it away.

    Guess what I found when I did an online search for “set arithmetic”? Absolutely nothing which supports your “methods”.

    So, again, remember that we don’t care about the values of the elements just how many there are: if the set of positive integers is larger than the set of positive even integers then there should be unmatched positive integers in the matching I proposed and is used in the Wikipedia article and lots of other places. Can you find any unmatched integers? Yes or no?

  235. 235
    JVL says:

    ET: Jerad sez that set subtraction doesn’t work with infinite sets. The problem is Jerad is a nobody and doesn’t get to make that decision. If there wasn’t any unmatched elements set subtraction would show that. And yet it shows the opposite.

    So, tell me which elements are unmatched. Go on.

    So it is clear that there are unmatched elements and no unmatched positions. Jerad cannot understand that.

    Which elements are unmatched? Tell me.

  236. 236
    ET says:

    The unmatched elements are all of those that set subtraction uncovers. It isn’t my fault that you are too stupid to understand that. Unbelievable. I can list the unmatched elements. I have listed the unmatched elements. You lose.

    Explain how it works with the positive multiples of 7 compared to the positive prime numbers.
    Already have. Your willful ignorance is your problem. Not mine

    Set subtraction is the wrong way to deal with the size of the sets!

    YOU don’t get to say that.

  237. 237
    ET says:

    The unmatched elements are all of those that set subtraction uncovers. It isn’t my fault that you are too stupid to understand that. Unbelievable. I can list the unmatched elements. I have listed the unmatched elements. You lose.

    Explain how it works with the positive multiples of 7 compared to the positive prime numbers.

    Already have. Your willful ignorance is your problem. Not mine. Stay focused on this discussion.

    Set subtraction is the wrong way to deal with the size of the sets!

    YOU don’t get to say that.

  238. 238
    JVL says:

    ET: The unmatched elements are all of those that set subtraction uncovers. It isn’t my fault that you are too stupid to understand that. Unbelievable. I can list the unmatched elements. I have listed the unmatched elements. You lose.

    You mean the odd integers? I can tell you what those are matched with! Again, here’s the scheme:

    J = the set of positive integers, E = the set of positive even integers.

    “1” from J is matched with “2” from E
    “2” from J is matched with “4” from E
    “3” from J is matched with “6” from E
    “4” from J is matched with “8” from E
    etc

    Gee, it looks like all the odds in J are matched up with something in E. “5” in J will be matched with “10” from E, “7” from J will be matched with “14” from E, “123” from J will be matched with “246” from E. Easy.

    So, which elements from J are unmatched? I’m not seeing any. Do show me a list.

    Already have. Your willful ignorance is your problem. Not mine. Stay focused on this discussion.

    Really? Which set is bigger, the set of the positive multiples of 7 or the set of the positive primes?

    YOU don’t get to say that.

    Oh dear! Will that go down on my permanent record?

  239. 239
    ET says:

    Guess what I found when I did an online search for “set arithmetic”? Absolutely no one uses the concept that all countably infinite sets have the same cardinality. It’s as useless as the people saying it. 😛

  240. 240
    ET says:

    J = the set of positive integers, E = the set of positive even integers.

    D = the positive set of odd integers.

    J-E=D, The entire set of positive odd integers is left unmatched. You lose, again.

  241. 241
    ET says:

    Already have. Your willful ignorance is your problem. Not mine. Stay focused on this discussion.

    Really?

    Really, really. Grow up or stuff it, Jerad.

  242. 242
    JVL says:

    ET: Guess what I found when I did an online search for “set arithmetic”? Absolutely no one uses the concept that all countably infinite sets have the same cardinality. It’s as useless as the people saying it. ????

    Oh dear, guess we’d better throw out all those textbook and papers based on set theory. What a shame.

    J-E=D, The entire set of positive odd integers is left unmatched. You lose, again.

    Ah, no. I just told you:

    “1” in J is matched with “2” in E
    “3” in J is matched with “6” in E
    “5” in J is matched with “10” in E
    “7” in J is matched with “14” in E
    and so on.

    Do try an pay attention or you’ll have to sit in the naughty corner.

    So, you still haven’t found any unmatched elements of the positive integers using my scheme. Maybe there aren’t any . . . you did admit it was one-to-one . . . and it is onto as well . .. gosh, I guess the sets are the same size! Hooray!!

  243. 243
    Jim Thibodeau says:

    ET, when every single mathematician in the world disagrees with you about very basic math concepts, you might want to consider the possibility that….

  244. 244
    Ed George says:

    I know absolutely nothing about set theory but I do know when someone is getting his ass handed to him. And I also know when someone is too narcissistic to acknowledge that they may be wrong. This thread would make a perfect case study of both.

  245. 245
    ET says:

    JVL:

    Oh dear, guess we’d better throw out all those textbook and papers based on set theory.

    Spoken like a totally ignorant ass. Nicely done, loser.

    J-E=D, The entire set of positive odd integers is left unmatched. You lose, again.

    Set subtraction refutes you, Jerad.

  246. 246
    ET says:

    Jimbo:

    ET, when every single mathematician in the world disagrees with you about very basic math concepts,

    Set subtraction is a basic math concept, you ignorant tool.

  247. 247
    ET says:

    Acartia Eddie:

    I know absolutely nothing

    This is true. But you didn’t have to say it as your posts prove it.

  248. 248
    ET says:

    Guess what I found when I did an online search for “set arithmetic”? Absolutely no one uses the concept that all countably infinite sets have the same cardinality. It’s as useless as the people saying it.

    And all Jerad can do is whine about set theory like a loser. How desperate do you have to be to think that the topic under discussion is all of set theory?

  249. 249
    ET says:

    Jerad can’t even follow his own blatherings:

    “1” in J is matched with “2” in E
    “3” in J is matched with “6” in E
    “5” in J is matched with “10” in E
    “7” in J is matched with “14” in E
    and so on.

    So there isn’t any “4” in the set of positive evens? No “8”- no “12”? Really? There isn’t any “2” in the set of positive integers? No “4”- no “6”? Really?

    Thank you for proving that you are a loser, Jerad.

  250. 250
    ET says:

    So, you still haven’t found any unmatched elements of the positive integers using my scheme.

    Why would I use your scheme? It is obviously the wrong tool for the job. 😛

  251. 251
    JVL says:

    ET: So there isn’t any “4” in the set of positive evens? No “8”- no “12”? Really? There isn’t any “2” in the set of positive integers? No “4”- no “6”? Really?

    Oh dear, ET is really not paying attention. I was just addressing his(?) claim that the odd-positive integers were unmatched in my scheme so I just repeated that part of the scheme. I thought he was paying attention. I’ll re-iterate the whole scheme, again.

    J = the set of positive integers. E = the set of positive even integers. Here’s the scheme:

    “1” in J is matched with “2” in E
    “2” in J is matched with “4” in E
    “3” in J is matched with “6” in E
    “4” in J is matched with “8” in E
    “5” in J is matched with “10” in E
    “6” in J is matched with “12” in E
    “7” in J is matched with “14” in E
    “8” in J is matched with “16” in E
    “9” in J is matched with “18” in E
    “10” in J is matched with “20” in E
    and so on!

    So, each and every positive integers is matched with one and only one element in the positive even integers. AND each and every positive even integers is matched with one and only one element in the positive integers. Is there anything unmatched? I can’t see one. How could that happen if one set was bigger than the other? Gosh, I don’t think it could happen. I guess the sets are the same size!

    Why would I use your scheme? It is obviously the wrong tool for the job. ????

    It does what I want. It’s a one-for-one matching between all the elements of the positive integers and all the elements of the positive even integers. And it’s not disallowed so . . . yup, I’m good with it.

    And all Jerad can do is whine about set theory like a loser. How desperate do you have to be to think that the topic under discussion is all of set theory?

    Do you have any idea how large all of set theory is? The stuff we’re talking about is in the first part of chapter one of any standard textbook. And much of the rest follows. But you know that because you’ve studied set theory haven’t you? What was the textbook again? I can’t remember what you said. Oh, that’s right, you didn’t say!

    So, once again, can you find an unmatched element in my matching between the positive integers and the positive even integers? Yes or no? I’ve stated it over and over and over again. And you’ve made up issues like “contrived vs derived” and “standard matching” none of which have turned out to be real issues. All you have to do now is answer yes or no. Under my scheme are there any unmatched elements of either set? Yes or no?

  252. 252
    Jim Thibodeau says:

    ET math

    {1+2+3….} = {1+3+5…} + {2+4+6…}
    Infinity = Infinity + Infinity

    1*Infinity = 2*Infinity

    Cross out like terms,

    1 = 2

    Wow!!! ET you’re going to win The Fields Medal!!!!

  253. 253
    JVL says:

    1*Infinity = 2*Infinity

    Don’t get me started . . . I have chosen not mention the fact that there are different sizes of infinity. We’ll save that for another life time it appears.

  254. 254
    ET says:

    Yes, Jimmy, your desperation knows no bounds. I never said anything about adding infinities, loser.

  255. 255
    ET says:

    JVL:

    I have chosen not mention the fact that there are different sizes of infinity.

    There is only ONE infinity. It can be populated with differing densities of elements.

  256. 256
    ET says:

    JVL:

    Do you have any idea how large all of set theory is?

    Yes, I do. And that is why you are a wanker for saying what you did.

    Set subtraction proves that the set of positive integers contains more elements than the set of positive even integers. That means it proves that your matching scheme is the wrong tool for the job. And set subtraction proves your scheme doesn’t work.

  257. 257
    JVL says:

    ET: Yes, Jimmy, your desperation knows no bounds. I never said anything about adding infinities, loser.

    You agree that the positive integers are comprised of the combination of the positive even integers and the positive odd integers yes? So you are adding infinities . . .

    In your system the cardinality of the integers is equal to the sum of the cardinality of the evens and the cardinality of the odds.

    So that means 1 x infinity = 2 x infinity.

    Does that mean that 1 = 2?

    (by the way, Cantor figured out how to handle this . . . just sayin’)

  258. 258
    ET says:

    Guess what I found when I did an online search for “set arithmetic”? Absolutely no one uses the concept that all countably infinite sets have the same cardinality. It’s as useless as the people saying it.

    And only a desperate loser would think that means we have to throw out set theory. Enter Jerad…

  259. 259
    ET says:

    JVL:
    You agree that the positive integers are comprised of the combination of the positive even integers and the positive odd integers yes? So you are adding infinities . . .
    LoL! Adding the ELEMENTS, not infinities. It’s as if you are proud to prove that you are an ass.

  260. 260
    ET says:

    Everyone agrees that the positive integers are comprised of the combination of the positive even integers and the positive odd integers yes. You have to be a complete dolt to deny it.

  261. 261
    ET says:

    JVL:

    In your system the cardinality of the integers is equal to the sum of the cardinality of the evens and the cardinality of the odds.

    Yes

    So that means 1 x infinity = 2 x infinity.

    Only if you are an idiot. Are you an idiot, Jerad? You definitely make a strong case for it.

  262. 262
    JVL says:

    ET: There is only ONE infinity. It can be populated with differing densities of elements.

    So, what’s the cardinality of the rational numbers? Of the real numbers? Of the transcendental numbers?

    Yes, I do. And that is why you are a wanker for saying what you did.

    What, for asking you to find an unmatched element under my scheme? Pardon me!!

    Set subtraction proves that the set of positive integers contains more elements than the set of positive even integers. That means it proves that your matching scheme is the wrong tool for the job. And set subtraction proves your scheme doesn’t work.

    Find an unmatched element in my scheme. You can’t. That means your idea of how it all works is wrong. Doubling down on a bogus system doesn’t give you the win. Not being able to support your idea (that the the set of positive integers is bigger than the set of positive even integers) by finding an unmatched element means you’ve lost.

    Congratulations for going down with the sinking ship though. I’m not sure why you would do that but you clearly are committed.

  263. 263
    JVL says:

    ET: Everyone agrees that the positive integers are comprised of the combination of the positive even integers and the positive odd integers yes. You have to be a complete dolt to deny it.

    I’m not denying that, you really are not paying attention. I’m saying that all three sets have the same cardinality.

    Only if you are an idiot. Are you an idiot, Jerad? You definitely make a strong case for it.

    That’s what your system of “relative cardinality” says!! You should pay attention to what you’ve said.

    Can you find an unmatched element of either set in my matching? Yes or no?

  264. 264
    ET says:

    JVL:

    I’m saying that all three sets have the same cardinality.

    And yet set subtraction proves that they don’t.

    That’s what your system of “relative cardinality” says!!

    Only if you are an idiot. And here you are.

    My system is reflected by the one used to determine bijective functions. So clearly you are an ass.

  265. 265
    ET says:

    Jerad, look, you are an imbecile. You can’t even follow the discussion.

    Set subtraction uncovers unmatched elements.

    Doubling down on a bogus system doesn’t give you the win.

    And yet that is all you have ever done. Nice own goal.

    Set subtraction proves my point.

  266. 266
    ET says:

    There is only ONE infinity. It can be populated with differing densities of elements.

    So, what’s the cardinality of the rational numbers? Of the real numbers? Of the transcendental numbers?

    Each one has infinite elements. However, each has different densities of elements.

    But again, that is well over your limited thinking ability.

  267. 267
    Ed George says:

    The last 22 comments further supports my comment at 244.

  268. 268
    ET says:

    The comment @ 244, “Ed George” says:

    I know absolutely nothing

    And I agree

  269. 269
    ET says:

    Subtraction is the basic arithmetic operation used to determine if one thing is larger than the other.

    It doesn’t get any more foundational than that. So yes, I am going to question anyone who goes against what subtraction uncovers. And the “answer” I am getting is subtraction doesn’t work with sets of infinite elements- cuz it don’t, so there. Seriously.

    And because I have called out that explanation as total nonsense, I am the one getting something handed to him.

    How does that work?

  270. 270
    JVL says:

    ET: Set subtraction uncovers unmatched elements.

    But I can find matchings with no elements left out! I covered the odds so . . .

    Set subtraction proves my point.

    You haven’t found any unmatched elements in my scheme.

    There is only ONE infinity. It can be populated with differing densities of elements.

    Please link to some source which explains what that means.

    Each one has infinite elements. However, each has different densities of elements.

    Nope, wrong answer. The cardinality of the reals is greater than the cardinality of the integers, i.e. the real numbers are NOT countably infinite. But you studied set theory (what was the textbook used by the way, you haven’t answered yet) so you knew that.

    But again, that is well over your limited thinking ability.

    I’m happy for you to explain what that means mathematically. Some references would be nice.

    Subtraction is the basic arithmetic operation used to determine if one thing is larger than the other.

    It doesn’t work with some sets though does it? Like comparing the set of all multiples of 7 and the prime numbers. No help there.

    It doesn’t get any more foundational than that. So yes, I am going to question anyone who goes against what subtraction uncovers. And the “answer” I am getting is subtraction doesn’t work with sets of infinite elements- cuz it don’t, so there. Seriously.

    Whatever. I did give some examples where it doesn’t work but I guess you ignored those. I’m just thinking you haven’t been able to find any unmatched elements in my scheme for the positive integers and the positive even integers. If you can’t find one then the sets are the same size.

    And because I have called out that explanation as total nonsense, I am the one getting something handed to him.

    Dodging the fact that there is a long standing question you haven’t been able to answer.

    How does that work?

    ‘Cause you keep dodging questions and ignoring answers?

    People are really starting to notice and I don’t really intend to embarrass you any further but . . .

    Here’s a matching scheme for two infinite sets:

    Let J = the positive integers, let E = the positive even integers. Match them up with the following scheme:

    “1” from J is matched with “2” from E
    “2” from J is matched with “4” from E
    “3” from J is matched with “6” from E
    “4” from J is matched with “8” from E
    “5” from J is matched with 11.23 from E. Just kidding, “5” from J is matched with “10” from E
    “6” from J is matched with “12” from E
    “7” from J is matched with “14” from E
    “8” from J is matched with “16” from E
    “9” from J is matched with “18” from E
    “10” from J is matched with “20” from E
    “11” from J is matched with “22” from E
    and so on.

    Now, I may be wrong but it seems obvious to me that if you continue on in the same fashion that ever element in J is matched with one and only one element in E. And every element in E is matched with one and only one element in J. No element of either set is left out. In fact, if you specify a specific element of either set I will be able to tell you its “partner” in the other set. Both sets are well defined (I can easily tell you if something is in the set or not). The matching I am proposing matches the criteria listed well above for this sort of thing. And I keep asking . . .

    Given that matching the only way J or E is larger than the other is if there are some unmatched elements. So anyone who wants to say the two sets are not the same size only needs to find some elements that are unmatched. That’s all they’d have to do.

    So, can anyone find an element of J or E that is unmatched? Yes or no?

  271. 271
    ET says:

    JVL:

    But I can find matchings with no elements left out!

    And set subtraction proves your scheme is bogus!

    Please link to some source which explains what that means.

    That’s Cantor’s point with respect to different infinities.

    It doesn’t work with some sets though does it?

    Set subtraction is a real thing and it really works.

    Like comparing the set of all multiples of 7 and the prime numbers.

    It works just fine. And I have explained it to you. You are just an obtuse loser.

    And AGAIN- set subtraction proves your scheme is bogus. So just repeating yourself proves that you are an ass. Ignoring my answers doesn’t mean they weren’t provided.

    So if you are going to ignore what set subtraction uncovers and just keep repeating your nonsense, then there isn’t anything else to say.

  272. 272
    ET says:

    Each one has infinite elements. However, each has different densities of elements.

    Nope, wrong answer.

    No, it’s the right answer.

    The cardinality of the reals is greater than the cardinality of the integers, i.e. the real numbers are NOT countably infinite.

    Yes, I know. That is what differing densities means.

  273. 273
    ET says:

    Again, Jerad isn’t anyone to say that set subtraction cannot be applied to sets with infinite elements. There isn’t anything in any math text book that supports that lie.

    Cantor’s proof is for checking if the two sets are countably infinite. But being countably infinite doesn’t say anything about the cardinality.

  274. 274
    JVL says:

    ET: And set subtraction proves your scheme is bogus!

    Which means there would be some unmatched elements but you can’t find any.

    That’s Cantor’s point with respect to different infinities.

    I don’t think he mentioned different densities. Try again.

    Set subtraction is a real thing and it really works.

    Show how it works with these two sets:

    Let S = the set of the positive multiples of 7 and P = the set of positive prime numbers.

    I suspect you will ignore this but people will notice.

    t works just fine. And I have explained it to you. You are just an obtuse loser.

    You haven’t showed it working with those two sets.

    And AGAIN- set subtraction proves your scheme is bogus. So just repeating yourself proves that you are an ass. Ignoring my answers doesn’t mean they weren’t provided.

    You keep running away from answering a very long standing question: ;you have yet to find an unmatched element in my matching scheme. So the sets must the same size. Which means ‘set subtraction’ fails. End of.

    So if you are going to ignore what set subtraction uncovers and just keep repeating your nonsense, then there isn’t anything else to say.

    IF subtraction is correct then you should be able to find some unmatched elements. But you can’t so subtraction fails. End of.

    Each one has infinite elements. However, each has different densities of elements.

    Please give a rigorous mathematical explanation of what this means.

    The cardinality of the reals is greater than the cardinality of the integers, i.e. the real numbers are NOT countably infinite.

    Yes, I know. That is what differing densities means.

    So . . . the cardinality of the reals is greater than the cardinality of the integers? By how much?

    Again, Jerad isn’t anyone to say that set subtraction cannot be applied to sets with infinite elements. There isn’t anything in any math text book that supports that lie.

    Of course not, no one is going to waste time discussing something that doesn’t work! AND you haven’t found any reference supporting it. And you keep not answering the same question . . .

    Cantor’s proof is for checking if the two sets are countably infinite. But being countably infinite doesn’t say anything about the cardinality.

    You know what? Since no one is taking you seriously I’m not sure why I should keep arguing with you . . . Except that I think it makes a site like this look completely idiotic to not call one of its most prolific contributors on promulgating ridiculous notions. You looking foolish doesn’t matter that much. Uncommon Descent looking foolish hurts the cause. A lot. I bet people on other sites are laughing at you and UD right now.

  275. 275
    ET says:

    Set subtraction uncovers unmatched elements. Period. End of story.

    And I have already explained how it works with the sets Jerad mentions. But that is moot as Jerad can’t even grasp the basics. Until that happens there is no way he will be able to grasp anything else.

    YOUR MATCHING SCHEME IS BOGUS. What part of that are you too stupid to understand? Set subtraction uncovers the unmatched elements. What part of that are you too stupid to understand?

    Of course not, no one is going to waste time discussing something that doesn’t work!

    It works! Only a desperate loser says that it doesn’t. Math books tell you that dividing by 0 doesn’t work. So clearly Jerad is making things up because he can’t handle the truth.

    And I am not the one who uses the concept being disputed to try to settle the dispute. You are that fool.

    It still remains that absolutely no one uses the concept that all countably infinite sets have the same cardinality. It’s as useless as the people saying it. That’s you, Jerad.

  276. 276
    ET says:

    And if Jerad being a cowardly ass makes UD look foolish, then so be it. I say it reflects more on Jerad than it does on UD.

  277. 277
    JVL says:

    ET: Set subtraction uncovers unmatched elements. Period. End of story.

    But you can’t say what they are!! Too funny. I already covered the odds so you’ve got to find another answer.

    And I have already explained how it works with the sets Jerad mentions. But that is moot as Jerad can’t even grasp the basics. Until that happens there is no way he will be able to grasp anything else.

    Sorry but you did not say whether the multiples of 7 or the primes had a larger cardinality.

    YOUR MATCHING SCHEME IS BOGUS. What part of that are you too stupid to understand? Set subtraction uncovers the unmatched elements. What part of that are you too stupid to understand?

    You have provided no support for what you are saying. That means it’s only you saying so. Find an unmatched element or admit you can’t. The odds are matched. I showed you how.

    It works! Only a desperate loser says that it doesn’t. Math books tell you that dividing by 0 doesn’t work. So clearly Jerad is making things up because he can’t handle the truth.

    If it works it’s funny no one uses it for infinite sets. Puzzling that. Do you really want to talk about dividing by zero? I’m happy to do so.

    And I am not the one who uses the concept being disputed to try to settle the dispute. You are that fool.

    I’ve told ;you over and over and over again how to settle your ‘dispute’ but you keep failing to do so. Which means you can’t.

    It still remains that absolutely no one uses the concept that all countably infinite sets have the same cardinality. It’s as useless as the people saying it. That’s you, Jerad.

    It’s true regardless.

    And if Jerad being a cowardly ass makes UD look foolish, then so be it. I say it reflects more on Jerad than it does on UD.

    Of course the rest of the world doesn’t see it that way. The rest of the world says: look at that UD site, they can’t even get basic set theory right.

  278. 278
    ET says:

    JVL:

    But you can’t say what they are!!

    I provided a list!!!! Clearly you are a liar.

    Sorry but you did not say whether the multiples of 7 or the primes had a larger cardinality.

    Yes, you bare sorry. And yes I told you how to do it.

    You have provided no support for what you are saying.

    Of course I have

    If it works it’s funny no one uses it for infinite sets.

    You don’t know that.

    And I am not the one who uses the concept being disputed to try to settle the dispute. You are that fool.

    I’ve told ;you over and over and over again how to settle your ‘dispute’ but you keep failing to do so.

    Yes, you keep referring to the very thing being disputed. It’s as if you are proud to be a dolt.

    It still remains that absolutely no one uses the concept that all countably infinite sets have the same cardinality. It’s as useless as the people saying it. That’s you, Jerad.

    It’s true regardless.

    Not according to set subtraction.

    Of course the rest of the world doesn’t see it that way.

    Of course they do. They see an impotent person, who is unable to deal with the reality that ID has the science and he can’t refute it. So that person has to pick a fight over a topic he doesn’t understand.

    And what I am disputing is not basic set theory. They see that you can’t even get subtraction right!

  279. 279
    JVL says:

    ET: I provided a list!!!! Clearly you are a liar.

    And I showed you how the odds are matched! Are you even paying attention?

    Yes, you bare sorry. And yes I told you how to do it.

    No, you did not. Which has a higher cardinality: the positive multiples of 7 or the positive prime numbers?

    Of course I have

    Repeating the same thing over and over again is not support.

    You don’t know that.

    Well, you’ve been unable to provide any support for “set subtraction” so . . .

    And I am not the one who uses the concept being disputed to try to settle the dispute. You are that fool.

    I told you how to win your “dispute” and you can’t manage to do that. So there is no dispute.

    It still remains that absolutely no one uses the concept that all countably infinite sets have the same cardinality. It’s as useless as the people saying it. That’s you, Jerad.

    Not true but it doesn’t affect its truth.

    Not according to set subtraction.

    Find some unmatched elements in my matching. It’s not the odds, I showed you how those are matched.

    Of course they do. They see an impotent person, who is unable to deal with the reality that ID has the science and he can’t refute it. So that person has to pick a fight over a topic he doesn’t understand.

    Really? Why then has no one come to your defence on this thread? Why is it that kairosfocus, bornagain77, martin_r, News, Barry Arrington, Granville Sewell and all the rest have left you out to sway in the wind? Even they don’t agree with you.

    And what I am disputing is not basic set theory. They see that you can’t even get subtraction right!

    What set theory course did you take? What was the course number? Which university was it? Who was the author of the textbook?

  280. 280
    ET says:

    JVL:

    And I showed you how the odds are matched!

    Using a bogus scheme.And I showed you how the odds are matched!

    No, you did not.

    You are a liar. I showed and told you how to do it.

    Repeating the same thing over and over again is not support.

    And yet that is all you do.

    Well, you’ve been unable to provide any support for “set subtraction” so . .

    It’s used. There isn’t anything preventing anyone from using it on sets with infinite elements.

    set subtraction

    Find some unmatched elements in my matching.

    Why would I use the WRONG TOO, FOR THE JOB? Clearly you are an ass

    Why then has no one come to your defence on this thread?

    No one cares. Why hasn’t anyone come to your defense? Your two cheerleaders are just ignorant trolls.

    You are a liar and a toll, Jerad.

  281. 281
    JVL says:

    ET: Using a bogus scheme.And I showed you how the odds are matched!

    A bogus scheme? Are we back to your unsupported “contrived” stuff again? We are talking about the same matching used in a Wikipedia article. And you showed me how the odds are matched? Maybe you should just go lie down and give it a break.

    Being generous and assuming you meant you showed me that the odds are unmatched I have CLEARLY shown, twice, how they are matched. Try again.

    You are a liar. I showed and told you how to do it.

    No, I’d remember you coming up with a “relative cardinality” of the primes. You didn’t do it. Anyone can scan through the thread and see that. You’re starting to sound like Donald Trump, i.e. you’re making things up which the rest of the world knows is wrong.

    It’s used. There isn’t anything preventing anyone from using it on sets with infinite elements.

    You can use it. It doesn’t work with cardinalities but you can use it. Funny that no one else does.

    Ooooo, you linked to an elementary school level Venn diagram! Is that really the best you can do? That didn’t address cardinalities at all. You really are grasping.

    Why would I use the WRONG TOO, FOR THE JOB? Clearly you are an ass

    Because you cannot admit you are wrong. And you cannot identify unmatched elements between the positive integers and the positive even integers under my scheme. And don’t keep claiming you provided a list because I dealt with that and you were wrong as can be clearly seen.

    No one cares. Why hasn’t anyone come to your defense? Your two cheerleaders are just ignorant trolls.

    I don’t need any help; what I am saying matches what every textbook, every paper on set theory and every online resource says. And you can’t find any unmatched elements from the positive integers and the positive even integers using my matching scheme.

    You are a liar and a toll, Jerad.

    But I’m right. And you cannot find any unmatched elements between the positive integers and the positive even integers using my scheme.

  282. 282
    ET says:

    Yes, set subtraction proves that your scheme is bogus. You aren’t right. You are not even wrong.

    I linked to the website to prove that set subtraction is both useful and used. You lose.

    I don’t need any help;

    Clearly you do. All you can do is keep referring to the very thing I am disputing as if that settles the dispute. And I am sure that anyone reading this understands that what you are doing is foolish. Anyone who can use logic and reasoning, anyway.

    Set subtraction refutes your claim, Jerad. And just repeating your pap isn’t going to change that fact.

  283. 283
    ET says:

    And I’m right. You cannot find a one-to-one correspondence using the matching scheme used to determine unions, subsets and proper subsets.

    So here we are- we will just be repeating that for a while. 😛

  284. 284
    JVL says:

    ET: Yes, set subtraction proves that your scheme is bogus. You aren’t right. You are not even wrong.

    You’re not even trying to answer my matching question. That says it all really.

    I linked to the website to prove that set subtraction is both useful and used. You lose.

    One baby panel showing one simple situation and you think it’s all okay? hahahahahahahahahah

    Clearly you do. All you can do is keep referring to the very thing I am disputing as if that settles the dispute. And I am sure that anyone reading this understands that what you are doing is foolish. Anyone who can use logic and reasoning, anyway.

    Because you haven’t responded to the situation! I told you how to deal with your “dispute” and you failed. So the dispute is over.

    Set subtraction refutes your claim, Jerad. And just repeating your pap isn’t going to change that fact.

    You not being able to find an unmatched element between the positive integers and the positive even integers under my scheme shows you can’t back up your claims. And you’ve had plenty of time. You keep running in hopes the truth won’t catch up with you.

    And I’m right. You cannot find a one-to-one correspondence using the matching scheme used to determine unions, subsets and proper subsets.

    Here we go AGAIN! You think some matchings are allowed and some aren’t but you’ve NEVER been able to back that up. You keep recycling your unsupported arguments.

    So here we are- we will just be repeating that for a while. ????

    I’m good with you not being able to find an unmatched element between the positive integers and the positive even integers under my scheme, which is entirely fine. I’m good with being correct. I’m good with you ignoring the math, ignoring the arguments, ignoring the answers to your objections. But you’ve run out of room to run. Time to admit you’ve made a mistake.

    (I know you won’t admit you’re wrong and you’ll keep this going INTO infinity because you just cannot acknowledge that you are ever wrong.)

  285. 285
    ET says:

    You’re not even trying to answer my matching question.

    I SAID IT IS BOGUS, IE THE WRONG TOOL FOR THE JOB. I WOULD EXPECT ALL COUNTABLY INFINITE SETS TO BE ABLE TO BE PUT IN A ONE TO ONE CORRESPONDENCE. THAT IS BECAUSE THAT IS JUST A POSITION THING.

    One baby panel showing one simple situation and you think it’s all okay?

    I considered who I was providing it for.

    I told you how to deal with your “dispute” and you failed.

    Right. You told me to use the methodology that I am disputing. The methodology that set subtraction proves is bogus.

    You not being able to find an unmatched element between the positive integers and the positive even integers under my scheme shows you can’t back up your claims.

    Your scheme is bogus.

    And I’m right. You cannot find a one-to-one correspondence using the matching scheme used to determine unions, subsets and proper subsets.

    Why do we have to use yours when set subtraction contradicts it?

    So again, all Jerad can do is use the methodology I am disputing, to try to settle the dispute. You have serious issues, Jerad. Just because Jerad and his minions are unable to grasp what that means just proves how clueless they are.

    The world of textbooks are rife with examples of things being taught one way only to have that over turned. Jerad thinks that knowledge has to be stuck in the 19th century. And whines because I do not.

  286. 286
    ET says:

    I have acknowledge I was wrong many times. It isn’t my fault that you can only make your case by using the very thing I am saying is bogus.

  287. 287
    Jim Thibodeau says:

    Dang JVL, you’ve made someone very angry.

    http://intelligentreasoning.blogspot.com/

  288. 288
    ET says:

    JVL @ 125:

    What was true for Pythagoras and Euclid is still true.

    Because what the gave us was and is used. And proved true with real world applications. No one uses the concept that all countably infinite sets have the same cardinality. The concept doesn’t even make any sense.

    Can’t compare Euclid and Pythagoras to Cantor’s useless concept.

  289. 289
    ET says:

    Cheerleader Jimmie, waving his pom-poms. And lying. Always lying.

  290. 290
    Ed George says:

    ET

    I have acknowledge I was wrong many times.

    🙂 🙂 🙂

  291. 291
    ET says:

    Eddie “I know absolutely nothing” George. 🙂 🙂 🙂

  292. 292
    Jim Thibodeau says:

    Ed, you have to admit, ET’s just as good at biology as he is at math.

  293. 293
    Jim Thibodeau says:

    None of the ID scholars here disagree with ET on math, so I have to assume it’s of the same piece.

  294. 294
    Jim Thibodeau says:

    Do you suppose ET is a Darwinist who’s just trying to make ID people look like angry fools?

  295. 295
    JVL says:

    ET: I SAID IT IS BOGUS, IE THE WRONG TOOL FOR THE JOB. I WOULD EXPECT ALL COUNTABLY INFINITE SETS TO BE ABLE TO BE PUT IN A ONE TO ONE CORRESPONDENCE. THAT IS BECAUSE THAT IS JUST A POSITION THING.

    That’s exactly right, you are just matching up the elements regardless of their ‘value’. Well done! You got it. You can stop shouting now.

    Right. You told me to use the methodology that I am disputing. The methodology that set subtraction proves is bogus.

    You disputed it but you cannot point out a fault with it. AND it’s widely used. You lost that dispute.

    Your scheme is bogus.

    Of course you don’t like it! It shows that you are wrong. But that doesn’t make it incorrect.

    And I’m right. You cannot find a one-to-one correspondence using the matching scheme used to determine unions, subsets and proper subsets.

    Which is why I didn’t use it. I used a method that DOES exhibit the matching I’m trying to prove exists!! It’s allowed. Check out any website or textbook you like; you can use any scheme you like because it’s all about the number of elements NOT their values.

    So again, all Jerad can do is use the methodology I am disputing, to try to settle the dispute. You have serious issues, Jerad. Just because Jerad and his minions are unable to grasp what that means just proves how clueless they are.

    You lost the dispute because you can not find fault with it except to shout that it’s bogus. There is no dispute just you not wanting to admit you made a mistake.

    The world of textbooks are rife with examples of things being taught one way only to have that over turned. Jerad thinks that knowledge has to be stuck in the 19th century. And whines because I do not.

    Not in mathematics. what was true 2000 years ago is still true, what was true 1000 years ago is still true, what was true in the 19th century is still true. You really do not understand how mathematics works.

    I have acknowledge I was wrong many times. It isn’t my fault that you can only make your case by using the very thing I am saying is bogus.

    Because it’s not bogus, you lost the ‘dispute’.

    Because what the gave us was and is used. And proved true with real world applications. No one uses the concept that all countably infinite sets have the same cardinality. The concept doesn’t even make any sense. Can’t compare Euclid and Pythagoras to Cantor’s useless concept.

    YOU don’t use it so you think it’s useless. That doesn’t make it so. AND, regardless if there are read-world applications, that does not affect its truth.

  296. 296
    JVL says:

    Jim Thibodeau: Dang JVL, you’ve made someone very angry.

    I’ll struggle on, somehow.

    None of the ID scholars here disagree with ET on math, so I have to assume it’s of the same piece.

    Who knows? I’m sure Drs Dembski and Sewell agree with me.

    Do you suppose ET is a Darwinist who’s just trying to make ID people look like angry fools?

    No, he’s sincere.

  297. 297
    ET says:

    Jimmie:

    Ed, you have to admit, ET’s just as good at biology as he is at math.

    And I am better than you at both.

  298. 298
    ET says:

    JVL:

    That’s exactly right, you are just matching up the elements regardless of their ‘value’.

    Learn how to read. You are NOT matching the elements.

    You disputed it but you cannot point out a fault with it.

    LIAR. All I have done is pointe out its faults.

    AND it’s widely used.

    It is NOT use for anything. It is a useless concept.

    Of course you don’t like it!

    It’s not that I don’t like it. It’s BOGUS, you ignorant loser.

    Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance.

    And that all you can do is repeat what I am disputing proves that you are a willfully ignorant coward.

    Good luck with that. Let me know whenever you are able to think for yourself and can formulate an argument without using the disputed nonsense.

  299. 299
    ET says:

    If Granville agreed with Jerad then what is posted in comment 12 doesn’t say that. But then again not one of my detractors knows how to read for comprehension.

  300. 300
    ET says:

    JVL:

    Not in mathematics. what was true 2000 years ago is still true, what was true 1000 years ago is still true, what was true in the 19th century is still true.

    That only pertains to the math people can and have used. No one uses Cantor’s concept of all countably infinite sets have the same cardinality. It is useless without an application. And to top it off it is contradicted by at least two different models.

    You show me a math concept that has survived the centuries that is contradicted by two different models and I will listen to you

  301. 301
    Jim Thibodeau says:

    @JVL Sewell posts here sometimes, doesn’t he? Somebody should make a post where he and ET discuss this set theory business.

  302. 302
    ET says:

    What’s to discuss? I made my points. Perhaps at least Dr. Sewell would address them properly. I know that you cowards can’t.

    And again, it is all moot as the concept under dispute is useless and because of that, meaningless. But you are too dim to understand even that.

  303. 303
    Ed George says:

    JT

    Ed, you have to admit, ET’s just as good at biology as he is at math.

    He demonstrated his fundamental ignorance of math during his multi-year defence of his claim that Frequency = Wavelength.

  304. 304
    Jim Thibodeau says:

    ET seems reluctant to debate Sewell. Wonder why….

  305. 305
    JVL says:

    ET: Learn how to read. You are NOT matching the elements.

    Of course I am! I showed you the scheme. “Matching” just means pairing up. And I can do it the way I am doing it, it’s allowed.

    LIAR. All I have done is pointe out its faults.

    You said it was bogus, which is an opinion. You said your “set subtraction” contradicts it but no one else uses “set subtraction” when working with cardinalities. Your “set subtraction” can’t handle lots and lots of situations. My approach is used in many, many textbooks and on many, many sites because it’s allowed and it works, especially for this particular case.

    It is NOT use for anything. It is a useless concept.

    It’s true regardless.

    It’s not that I don’t like it. It’s BOGUS, you ignorant loser.

    I don’t remember ever reading a mathematical definition of bogus. Maybe I missed something.

    Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance.

    I understand that you are desperate to avoid admitting you’re wrong. I understand what hundreds of mathematicians have done working with such things. I understand why matching elements of sets one-for-one works to compare their cardinalities.

    And that all you can do is repeat what I am disputing proves that you are a willfully ignorant coward.

    You lost the dispute. I’ve told you why over and over and over again. Plus you cannot find anyone who says otherwise. There is no dispute, just you trying to score a point.

    Good luck with that. Let me know whenever you are able to think for yourself and can formulate an argument without using the disputed nonsense.

    I dispute your method and you continue to insist it’s true. So you have a double standard. Nicely done. Do they allow that in debates?

    That only pertains to the math people can and have used. No one uses Cantor’s concept of all countably infinite sets have the same cardinality. It is useless without an application. And to top it off it is contradicted by at least two different models.

    Of course it’s true!! Your fixation on applied mathematics is why you don’t get proofs and abstract work. Do you know how to design a complex electrical circuit using differential equations? Have you used complex variables to analyse fluid flow? Do you understand how prime numbers are used in cryptography? Have you found the volume of a solid of revolution using calculus? Have you found the eigenvalues of a muti-dimensional vector space? Have you found a Taylor series for a periodic function? Have you done triple integrals over volumes defined by surface functions? Have you actually done any higher level mathematics? You have to learn a lot of abstract principles before you get to the applications.

    You show me a math concept that has survived the centuries that is contradicted by two different models and I will listen to you

    None of the ones that have survived the centuries are contradicted. Some models have been refined (like physics moving from Newton to Einstein) but the math is all still true.

  306. 306
    Jim Thibodeau says:

    Fun questions!

    “Do you know how to design a complex electrical circuit using differential equations?”

    Let’s see…the capacitor is like a mass, and the inductor is like a spring…or the other way around… 😀

    “Have you used complex variables to analyse fluid flow?”

    No.

    ”Do you understand how prime numbers are used in cryptography?”

    Primes are the things you multiply together to get the keys if I recall correctly.

    “Have you found the volume of a solid of revolution using calculus?”

    That was Calc 2.

    “Have you found the eigenvalues of a muti-dimensional vector space?”

    Had to do that for advanced QM.

    “ Have you found a Taylor series for a periodic function?”

    Calc 2.

    “Have you done triple integrals over volumes defined by surface functions?”

    Calc 3.

    “Have you actually done any higher level mathematics?”

    Mostly Abstract Algebra.

  307. 307
    JVL says:

    Jim T: Mostly Abstract Algebra.

    Never liked that much. Grew to like Linear Algebra though after finding an excellent textbook. Didn’t spend nearly enough time on discrete topics; number theory is sublime.

  308. 308
    JVL says:

    Here’s a easy question for ET, please can no one else give the answer? Let’s see if he (?) can get it.

    What is the coefficient of the term a^3b^6 in the binomial expansion of (a + b)^7 ?

  309. 309
    JVL says:

    Here’s another good, basic question:

    Does the infinite series 2 + 4/3 + 8/9 + 16/27 + 32/81 . . . converge? If yes then to what?

    I loved infinite sequences and series. Really fun stuff. And heavily used in Talyor series and therefore a lot of analytic tools and situations.

  310. 310
    Jim Thibodeau says:

    @308 Jeez that’s an easy one.

  311. 311
    ET says:

    I dispute your method and Jerad continues to ay it’s true. I provide examples that contradict Jerad’s method and Jerad ignores them like the ignorant coward that he is.

  312. 312
    ET says:

    Now Jerad wants to try to change the discussion. That says it all. Jerad has proven ignorant of science. Jerad has proven to be ignorant of biology. And now Jerad has been proven to be the coward of mathematics.

  313. 313
    ET says:

    What is the coefficient of the term a^3b^6 in the binomial expansion of (a + b)^7 ?

    The binomial expansion of (a+b)^7 has several coefficients. There will be a 1 (twice), a 21, a -21, a 35, a -35, and a 7:

    a^7 – 7a^6xb+ 21a^5 x b^2 – 35a^4 x b^3 + 35a^3 x b^4 – 21a^2 x b^5 + 7ab^6 – b^7

  314. 314
    ET says:

    Acartia Eddie lies again:

    He demonstrated his fundamental ignorance of math during his multi-year defence of his claim that Frequency = Wavelength.

    Your quote mine proves that you are a clueless coward and a liar. Mt=y defense was only muliti-year because YOU ate too stupid to understand anything. Even Hazel and Jerad understood what I was saying. So clearly you are the loser, Acartia.

  315. 315
    ET says:

    JVL:

    Does the infinite series 2 + 4/3 + 8/9 + 16/27 + 32/81 . . . converge? If yes then to what?

    a=2; r= 2/3;(absolute) r< 1 S=a/(1-r); 2/(1-2/3) = 6 Yes, it converges to 6

  316. 316
    ET says:

    Do you know how to design a complex electrical circuit using differential equations? Have you used complex variables to analyse fluid flow? Do you understand how prime numbers are used in cryptography? Have you found the volume of a solid of revolution using calculus? Have you found the eigenvalues of a muti-dimensional vector space? Have you found a Taylor series for a periodic function? Have you done triple integrals over volumes defined by surface functions? Have you actually done any higher level mathematics? You have to learn a lot of abstract principles before you get to the applications.

    Yes, to all. What no one has ever done, you little wanker, is use the concept being debated for anything.

  317. 317
    ET says:

    Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance.

    And I understand that you are desperate to avoid those. But then again you clearly do NOT understand infinity.

  318. 318
    ET says:

    Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance.

    And I understand that you are desperate to avoid those. But then again you clearly do NOT understand infinity.

  319. 319
    ET says:

    Correction to 313- there are 2 7’s

  320. 320
    ET says:

    Jim Thibodeau seems reluctant to be truthful. I wonder why…

  321. 321
    JVL says:

    ET: I dispute your method and Jerad continues to ay it’s true. I provide examples that contradict Jerad’s method and Jerad ignores them like the ignorant coward that he is.

    I dispute your method and provide examples where it doesn’t work and you continue to use it. That’s a double standard.

    Now Jerad wants to try to change the discussion. That says it all. Jerad has proven ignorant of science. Jerad has proven to be ignorant of biology. And now Jerad has been proven to be the coward of mathematics.

    I just thought it would be interesting, you don’t have to play if you don’t want to.

    a^7 – 7a^6xb+ 21a^5 x b^2 – 35a^4 x b^3 + 35a^3 x b^4 – 21a^2 x b^5 + 7ab^6 – b^7

    Close, you screwed up some of the coefficients. Have another go.

    a=2; r= 2/3;(absolute) r< 1 S=a/(1-r); 2/(1-2/3) = 6 Yes, it converges to 6

    Very good. So you do agree that infinite sets exist and can be worked with. That’s good.

    How about this one:

    ! + (2^2)/2! + (3^3)/3! + (4^4)/4! + . . . Does it converge and if yes to what?

    Yes, to all. What no one has ever done, you little wanker, is use the concept being debated for anything.

    Ooo, very impressive. So you worked with infinite series yet you’re not sure infinite sets exist? Again, truth is not determined by the number of real world applications.

    Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance.

    My refusal to agree with you is because your system a) is not used, b) doesn’t work for a lot of sets and c) doesn’t give the same result as a system which IS used and DOES work for a lot of sets.

    And I understand that you are desperate to avoid those. But then again you clearly do NOT understand infinity.

    I’ll keep telling you why I disagree with you and your “method” if you like. I just thought you might be getting a bit bored.

    Even Hazel and Jerad understood what I was saying. So clearly you are the loser, Acartia.

    IF you have a fixed speed then a given wavelength will give a specific frequency and vice versa. Like two sets matched one-for-one isn’t it? Yes, it’s exactly like that. So, if the wave speed was, say, 1000 ft/sec then a frequency of 200 cycles per second would match up with a wavelength of 5 feet. So the wavelength and the frequency are not the same thing, but FOR A GIVEN SPEED one dictates the other. In fact, for a given speed you can match up, one-for-one elements from the frequency set with elements of the wavelength set. Which means both those sets have the same size! Get in!!

  322. 322
    ET says:

    JVL:

    I dispute your method and provide examples where it doesn’t work and you continue to use it.

    You are a LIAR.

    Close, you screwed up some of the coefficients.

    No, I didn’t.

    So you worked with infinite series yet you’re not sure infinite sets exist?

    I have explained that. Are you a retard?

    My refusal to agree with you is because your system a) is not used, b) doesn’t work for a lot of sets and c) doesn’t give the same result as a system which IS used and DOES work for a lot of sets.

    No one uses Cantor’s concept for anything. Mine works for all sets. YOU are too stupid to figure it out.

    IF you have a fixed speed then a given wavelength will give a specific frequency and vice versa.

    I know. Wavelength and frequency are interchangeable when discussing the emissions of CO2- you can talk about the frequency or the wavelength and you are discussing the SAME thing.

    Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance.

  323. 323
    ET says:

    All Jerad can do is continue to ignore reality and prattle on like a fool. And to top it off he is using the thing I am disputing to settle the dispute.

    How pathetic can you be, Jerad?

  324. 324
    JVL says:

    ET: You are a LIAR.

    Nope.

    No, I didn’t.

    Yeah, you did. Check the signs.

    I have explained that. Are you a retard?

    I’m just trying to understand what you think exists and what you don’t think exists.

    No one uses Cantor’s concept for anything. Mine works for all sets. YOU are too stupid to figure it out.

    Use your “concept” on the set of positive primes. What is the “relative cardinality” of the positive prime numbers? Here’s another one: what’s the “relative cardinality” of the set of the powers of 3? How about this: what’s the relative cardinality of the perfect squares?

    I know. Wavelength and frequency are interchangeable when discussing the emissions of CO2- you can talk about the frequency or the wavelength and you are discussing the SAME thing.

    BUT wavelength and frequency are NOT the same thing, we agree on that. For a fixed speed the wavelength will determine/dictate the frequency, yes? The emissions of CO2 . . . what frequency and wavelengths are you talking about? Visible light? Assuming that’s the issue then, I agree: you can refer to the “waves” in question either by their frequency ranges or their wavelength ranges because one determines the other. BUT they are NOT the same thing.

    Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance.

    I am allowed to disagree with you.

    All Jerad can do is continue to ignore reality and prattle on like a fool. And to top it off he is using the thing I am disputing to settle the dispute.

    But your method is disputed by every mathematician on the planet yet you keep using it. How is that fair?

    How pathetic can you be, Jerad?

    I’m not sure, I’ve never tried to figure that out. I’m not sure how to measure . . . pathetic-ness. And I’m not sure what scale to use. Interesting question.

  325. 325
    ET says:

    Ok I get it. See I admit when I made a mistake. Why I did (a-b)^7 is beyond me.

    Use your “concept” on the set of positive primes. What is the “relative cardinality” of the positive prime numbers? Here’s another one: what’s the “relative cardinality” of the set of the powers of 3? How about this: what’s the relative cardinality of the perfect squares?

    Again, I have explained ALL of that to you on my blog. I am not going over it again. It’s already been more than once.

    BUT wavelength and frequency are NOT the same thing,

    I never said they were. I said they are both representations of the SAME wave.

    Again, as I have told you, the CONTEXT was one person presenting papers on the absorption frequency of CO2 and the other was presenting papers on its wavelength. I was saying that it doesn’t matter because we are talking about the same thing.

    I am allowed to disagree with you.

    True, it’s the reason I am questioning. You can disagree that the Sun is a star, for all I care.

    But your method is disputed by every mathematician on the planet yet you keep using it.

    I haven’t shown it to any mathematician.

  326. 326
    Jim Thibodeau says:

    ”I haven’t shown it to any mathematician”

    That tells the whole story.

  327. 327
    ET says:

    LoL! @ Jimmie- No one uses the concept for anything. No one. It’s meaningless. So why bother?

    The only people I see arguing it are blog people.

  328. 328
    JVL says:

    ET: Ok I get it. See I admit when I made a mistake. Why I did (a-b)^7 is beyond me.

    I don’t know either. It happens. It was just a mistake. To be honest, I couldn’t figure out how you got the rest of it right and mucked up the signs!! That’s why I suggested you have another look. No one would get that much right and mess up the signs if they didn’t know what they were doing.

    Again, I have explained ALL of that to you on my blog. I am not going over it again. It’s already been more than once.

    But people haven’t seen those explanations here, probably worth repeating so they know you can handle those cases. it’s your call.

    I never said they were. I said they are both representations of the SAME wave.

    I agree with that characterisation. I don’t remember the argument that well but what you’re saying now I agree with.

    Again, as I have told you, the CONTEXT was one person presenting papers on the absorption frequency of CO2 and the other was presenting papers on its wavelength. I was saying that it doesn’t matter because we are talking about the same thing.

    Yup, fine with me. If someone else remembers things differently then I leave it to them to bring that. But I’m good.

    I haven’t shown it to any mathematician.

    Why not? No matter how much I argue with you you are clearly firm in your conviction. I would think you would give it a go and see if anyone agrees with you. You know my opinion but . . .

  329. 329
    ET says:

    No one uses the concept for anything. No one. It’s meaningless. So why bother?

    If you were to ask anyone on the street they would probably agree with me. So I’m OK with my homies’ support

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