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

Am Sun, 19 Jan 2025 11:47:50 +0100 schrieb WM:

On 18.01.2025 14:46, Richard Damon wrote:

On 1/17/25 4:56 PM, WM wrote:

 

That "definition" violates to definition that set don't change.

So it is. But if infinity is potential, then we cannot change this in
order to keep set theory, but then set theory is wrong.

So, you are just agreeing that your logic is based on contradictory
premsises and thus is itself contradictory and worthless.

Yes, with mutable sets.

No, set theory claims actual infinity but in fact useses potential
infinity with its "bijections".

"Set theory" uses neither.

They contain only natnumbers which have ℵ₀ successors.

There are no naturals with a finite number of successors, otherwise
you could count backwards from the end.

If all natural numbers were applied, there would not be
successors: ℕ \ {1, 2, 3, ...} = { }.

There are no successors if only you would actually "apply" the infinitely
many naturals.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.