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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
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.JVL
March 13, 2020
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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.ET
March 13, 2020
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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 nobodyET
March 13, 2020
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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.JVL
March 13, 2020
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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.ET
March 13, 2020
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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.ET
March 13, 2020
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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.ET
March 13, 2020
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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.JVL
March 13, 2020
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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.kairosfocus
March 12, 2020
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J T
Is nobody here going to support ET? Nobody?
I was going to wait until this thread had 200 comments.Ed George
March 12, 2020
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Is nobody here going to support ET? Nobody?Jim Thibodeau
March 12, 2020
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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.ET
March 12, 2020
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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.ET
March 12, 2020
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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.JVL
March 12, 2020
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Counter A will ALWAYS and FOREVER have a higher count than counter B. ALWAYS and FOREVER, which means for infinity.ET
March 12, 2020
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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.ET
March 12, 2020
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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.JVL
March 12, 2020
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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?ET
March 12, 2020
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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.ET
March 12, 2020
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`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!JVL
March 12, 2020
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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.JVL
March 12, 2020
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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."ET
March 12, 2020
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One definition of infinity is “the amount of time we will be waiting before any mathematician, anywhere in the multiverse, agrees with ET.”Jim Thibodeau
March 12, 2020
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" 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-websterET
March 12, 2020
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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.ET
March 12, 2020
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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.htmlET
March 12, 2020
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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 . . .JVL
March 12, 2020
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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.ET
March 12, 2020
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Yes, your ignorance of infinity and your ignorance of the English language don't make any sense at all.ET
March 12, 2020
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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.JVL
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Mar
12
12
2020
08:35 AM
8
08
35
AM
PDT
1 3 4 5 6 7 11

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