Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 1/21/25 6:10 AM, WM wrote:

On 20.01.2025 19:07, Richard Damon wrote:

On 1/20/25 7:33 AM, WM wrote:

On 19.01.2025 14:29, FromTheRafters wrote:

WM formulated the question :

On 19.01.2025 11:42, FromTheRafters wrote:

WM presented the following explanation :

On 18.01.2025 12:03, joes wrote:

Am Fri, 17 Jan 2025 22:56:13 +0100 schrieb WM:

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Correct. If infinity is potential. set theory is wrong.

And that is why set theory doesn't talk about "potential infinity".

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Nevertheless it uses potential infinity.

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No, it doesn't.

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Use all natnumbers individually such that none remains. Fail.

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This makes no sense.

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It is impossible.

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Because logic that insists on dealing with an INFINITE set one by one is illogical

 Yes. Therefore only the elements of a (potentially in-) finite set can be dealt with individually, i.e., one by one.

In 9ther words, you just agreed that my statment was correctm and thus your logic, which only deals with things one by one, is just illogical, EVEN for potential infinity, as you can't JUST deal with potential infinity one by one and expect to be able to complete in finite work,

 

Every element of the bijection has almost all elements as successors. Therefore the bijection is none.

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Nope, the logic that can't see the completion at infinity is broken.

 You contradict yourself. Bijections need individual elements.

Yea, it match individual elements but also look that the ENTIRE mapping at once.
This difference is something that you apparently can't see, because you are too stupid.
We establish the pattern individually, and then show that the pattern can be repeated indefinitely, and thus the matching happens as a collective whole. It can't complete if you don't move from the individual step to the collective step.
It needs to be able to move from "for any" n, to "for all", which is NOT an "individual, one by one" operation.

 Regards, WM