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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Wed, 4 Dec 2024 15:00:58 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Wed, 04 Dec 2024 14:31:12 +0100 schrieb WM:
> 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.
Please expand how this works in the infinite case.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.