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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?

Comments
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. :razz:ET
March 14, 2020
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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?JVL
March 14, 2020
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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.ET
March 14, 2020
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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.
ET
March 14, 2020
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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.JVL
March 14, 2020
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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?JVL
March 14, 2020
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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.ET
March 14, 2020
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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.ET
March 14, 2020
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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 trollET
March 14, 2020
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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.JVL
March 14, 2020
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@ 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?ET
March 14, 2020
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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.ET
March 14, 2020
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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.ET
March 14, 2020
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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 possibilityET
March 14, 2020
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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.ET
March 14, 2020
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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?JVL
March 13, 2020
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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.JVL
March 13, 2020
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@JVL if you really want to cause ET to have issues, bring up the Riemann Rearrangement Theorem. He might have a cerebral event. :-)Jim Thibodeau
March 13, 2020
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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.ET
March 13, 2020
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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.ET
March 13, 2020
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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.JVL
March 13, 2020
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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.JVL
March 13, 2020
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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.ET
March 13, 2020
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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.ET
March 13, 2020
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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.JVL
March 13, 2020
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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.ET
March 13, 2020
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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.ET
March 13, 2020
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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.JVL
March 13, 2020
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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.ET
March 13, 2020
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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?ET
March 13, 2020
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