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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: Mon, 02 Dec 2024 14:13:40 -0500
Organization: Peripheral Visions
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WM formulated on Monday :
> On 02.12.2024 16:46, FromTheRafters wrote:
>> WM wrote :
>
>>> E(1), E(2), E(3), ...
>>> and
>>> E(1), E(1)∩E(2), E(1)∩E(2)∩E(3), ...
>>> are identical for every n and in the limit because
>>> E(1)∩E(2)∩...∩E(n) = E(n).
>> 
>> Non sequitur. That which is true for finite sequences is not necessarily 
>> true for infinite sequences.
>
> As easily can be obtaied from the above it is necessarily true that up to 
> every term 

Yes, your nth term is the term common to all previous sets as members 
of the sequence. This final 'n' is always a member of the naturals. For 
infinite sets of naturals, there is no last element to be common to all 
previous sets, so it, the intersection, is empty.

> and therefore also in the limit the sequences of endsegments and 
> of intersections are identical.

Says you, but you can't prove the conjecture.

> Every contrary opinion is matheology, outside 
> of mathematics.

Says you, but you have little credibility here concerning mathematics.