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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Mon, 16 Dec 2024 07:30:30 -0500
Organization: i2pn2 (i2pn.org)
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On 12/16/24 3:27 AM, WM wrote:
> On 15.12.2024 21:20, joes wrote:
> 
>> Duh. All naturals are finite. You need to actually remove all inf.many
>> of them.
> 
> That is not possible with definable naturals:
> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> And numbers which succeed
> ∀k ∈ ℕ: ∩{E(1),E(2),...,E(k+1)} = ∩{E(1),E(2),...,E(k)}\{k}
> produce finite endsegments and therefore are invisible.
> 
> Regards, WM

Of course it is possible with the definable naturals, you just need to 
do the INFINITE number of steps, which your logic can't do.

Your finite logic just blows itself up into smithereens, leaving behind 
the darkness of its inconsistencies.