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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: Thu, 5 Dec 2024 09:39:10 +0100
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On 04.12.2024 19:06, FromTheRafters wrote:
> WM laid this down on his screen :

>> In two sets A and B which are non-empty both but have an empty 
>> intersection, there must be at least two elements a and b which are in 
>> one endsegment but not in the other:
>> a ∈ A but a ∉ B and b ∉ A but b ∈ B.
> 
> Finite thinking.

Correct thinking is always valid.
> 
>> Same with a set of endsegments.
> 
> No, because they are infinite and have no last element to be in every 
> participating endsegment.

But they have all elements, all of which are finite and obey
E(1)∩E(2)∩...∩E(n) = E(n).
If all endsegments are non-empty, then they have a non-empty 
intersection unless the above condition holds.

Regards, WM