My Math Forum Cantor's Diagonal Argument and Infinity

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March 20th, 2018, 07:21 AM   #21
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Quote:
 Originally Posted by zylo I assumed respondents would be familiar with Cantors infinite sequences {wiki), This sequence is either finite, 1001101010011, or infinite 1001101010011................. (endless). Endless means you can't get to the end, ie, you can't complete CDA. I assume all irrelevant replies (such as parts of speech-I said synomous) are a confirmation of this.
Sorry, but it is up to you to make your post as readable and informative as possible. You may find it readable enough for yourself, fine. But I think you're the only one whom you're making sense to, sadly. Try to bring yourself down to our level. Try to make yourself clear to us, and then we can have a cool discussion!

March 20th, 2018, 08:27 AM   #22
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Quote:
 Originally Posted by Micrm@ss Sorry, but it is up to you to make your post as readable and informative as possible. You may find it readable enough for yourself, fine. But I think you're the only one whom you're making sense to, sadly. Try to bring yourself down to our level. Try to make yourself clear to us, and then we can have a cool discussion!
Does Cantor's infinite sequence of binary digits end or not?

There are two possibilities: Yes or No.

March 20th, 2018, 10:19 AM   #23
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Quote:
 Originally Posted by zylo Does Cantor's infinite sequence of binary digits end or not?
That's not a useful question.

March 20th, 2018, 10:20 AM   #24
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 Originally Posted by zylo Does Cantor's infinite sequence of binary digits end or not? There are two possibilities: Yes or No.
No, it does not end.

March 20th, 2018, 06:55 PM   #25
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Quote:
 Originally Posted by zylo Endless means you can't get to the end, ...
Yes, it does. But...
Quote:
 ... ie, you can't complete CDA.
This doesn't follow. Cantor's Diagonal Argument is not a process that must complete. And your continued assertions about "ending" just prove that you do not understand anything about set theory.

For example, s(n)=mod(n,2) for all n in $\mathbb N$ is a pefectly valid definition of one of Cantor's strings. It does not end.

Last edited by JeffJo; March 20th, 2018 at 06:59 PM.

March 21st, 2018, 06:47 AM   #26
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Quote:
 Originally Posted by JeffJo Cantor's Diagonal Argument is not a process that must complete.
If it doesn't complete, it doesn't prove anything.

March 21st, 2018, 07:22 AM   #27
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Quote:
 Originally Posted by zylo If it doesn't complete, it doesn't prove anything.
There we have it. Zylo is thinking about a finite list.

There is not only no necessity that the list end, but it is explicitly an endless list because it is matched one-to-one to the assumedly endless positive integers.

There is nothing wrong with denying the acceptability of infinity, but doing so makes it ridiculous to discuss Cantor's diagonal theorem, which proves that, if infinity is accepted, then infinity is not a single, undifferentiated concept

March 21st, 2018, 09:27 AM   #28
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Quote:
 Originally Posted by zylo If it doesn't complete, it doesn't prove anything.
He never said that "it doesn't complete" he said "it's not a process".

March 21st, 2018, 11:05 AM   #29
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Quote:
 Originally Posted by zylo If it doesn't complete, it doesn't prove anything.
One wouldn't expect an endless string to be a proof. Cantor's argument does end - it isn't endless on account of its use of endless strings.

March 21st, 2018, 06:02 PM   #30
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Quote:
 Originally Posted by zylo If it doesn't complete, it doesn't prove anything.
Quote:
 Originally Posted by JeffJo For example, s(n)=mod(n,2) for all n in $\mathbb N$ is a pefectly valid definition of one of Cantor's strings. It does not end.
Do you think the emphasized statement defines every character in an endless string, or do you think it does not?

If "not," in what place do you think it fails? And why?

Cantor's strings are not defined by a process that must end to define every character. Just like the Axiom of Infinity defines every natural number in $\mathbb N$ - and establishes BY AXIOM that it is possible to do so - every character of that string is defined by a single statement. Without needing a process that ends.

 Tags argument, cantor, cantors, diagonal, infinity

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