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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: Wed, 4 Dec 2024 16:21:57 +0100
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On 04.12.2024 16:00, joes wrote:
> Am Wed, 04 Dec 2024 14:31:12 +0100 schrieb WM:

>> 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.
>> Same with a set of endsegments. It can be divided into two sets for both
>> of which the same is required.
> Please expand how this works in the infinite case.
> 
In every case of empty intersection of non-empty sets at least two such 
elements must exist. Important is not whether there are few or 
infinitely many infinite sets but only that the intersection is empty.

Regards, WM