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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: Tue, 7 Jan 2025 13:07:20 +0100
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On 07.01.2025 12:36, Alan Mackenzie wrote:

> If there were such
> things as "potential" and "actual" infinity in maths,

Your comments about my quotes show that you have lost all contact with 
mathematics.

  then they would
> make a difference to some mathematical result.

Of course. Here is a simple example, accessible to every student who is 
not yet stultified by matheology.

For the inclusion-monotonic sequence of endsegments of natural numbers 
E(k) = {k+1, k+2, k+3, ...} the intersection of all terms is empty. But 
if every number k has infinitely many successors, as ZF claims, then the 
intersection is not empty. Therefore set theory, claiming both, is false.

Inclusion monotonic sequences can only have an empty intersection if 
they have an empty term. Therefore the empty intersection of all 
requires the existence of finite terms which must be dark.

Further there are not infinitely many infinite endsegments possible 
because the indices of an actually infinite set of endsegements without 
gaps must be all natural numbers.

Regards, WM