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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 19 Jan 2025 15:10:50 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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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.

-- 
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.