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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Tue, 26 Nov 2024 09:45:36 +0100
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On 26.11.2024 06:58, Jim Burns wrote:
> On 11/25/2024 8:52 AM, WM wrote:

>> Finite cardinalities belong to dark endsegments.
> 
> Finite cardinals can change by 1

Yes. The last endsegments have 3, 2, 1, 0 elements.
> 
> Each end.segment Eᶠⁱⁿ(k) of the finite.cardinalities ℕᶠⁱⁿ
> holds a countable.to.from.0 least.element

No. All elements of finite endsegments  (and almost all of infinite 
endsegments) are dark.
>> The endsegments
>> only can have an empty intersection
>> if there are endsegments with 3, 2, 1, 0 elements.
> 
> The end.segments
> can only have a non.empty intersection
> if there is an element which is in each end.segment.

That is the case for every non-empty endsegment before all elements are 
lost.

Otherwise two endsegments with different elements must exist. That is 
impossible by inclusion monotony.

Regards, WM