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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Wed, 04 Dec 2024 13:06:23 -0500
Organization: Peripheral Visions
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WM laid this down on his screen :
> 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.

Finite thinking.

> Same with a set of endsegments.

No, because they are infinite and have no last element to be in every 
participating endsegment.

> It can be divided into two sets for both of 
> which the same is required.