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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Fri, 29 Nov 2024 22:54:13 +0100
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On 29.11.2024 22:36, Jim Burns wrote:

> The end.segments are infinite.
> Their intersection is empty.

Contradiction in terms of inclusion monotony! The intersection is an 
endsegment.
> Nothing is infinite and empty.
> 
Up to every infinite endsegment E(n) the index n is finite and the 
intersection is infinite.
∀k ∈ ℕ_def: ∩{E(1), E(2), ..., E(k)} = E(k).

There is no infinite set of indices in ℕ followed by the infinite 
contents of endsegments. Therefore there is no infinite set of infinite 
endsegments possible. Either the set of indices is infinite, then the 
remaining contents is empty, or the remaining contents is infinite, then 
the set of indices is finite.

Try to show a counter example: Infinitely many indices and 
simultaneously infinite remainig contents.

Regards, WM