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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 14:31:12 +0100
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On 04.12.2024 11:33, FromTheRafters wrote:
> WM formulated the question :
>> On 03.12.2024 21:34, Jim Burns wrote:
>>> On 12/3/2024 8:02 AM, WM wrote:
>>
>>>> E(1)∩E(2)∩...∩E(n) = E(n).
>>>> Sequences which are identical in every term
>>>> have identical limits.
>>>
>>> An empty intersection does not require
>>>   an empty end.segment.
>>
>> A set of non-empty endsegments has a non-empty intersection. The 
>> reason is inclusion-monotony.
> 
> Conclusion not supported by facts.

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.

Regards, WM