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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: Sat, 30 Nov 2024 15:58:52 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 30 Nov 2024 13:19:46 +0100 schrieb WM:
> On 30.11.2024 12:54, FromTheRafters wrote:
> 
>> Finite sets versus infinite sets. Finite ordered sets have a last
>> element which can be in the intersection of all previously considered
>> finite sets. Infinite ordered sets have no such last element.
> But they have infinitely many elements which contribute to the
> intersection.
For an intersection, the "smallest" set matters, which there isn't
in this infinite sequence, only a "biggest". 

> The intersection of the "finite initial segment" of endsegments is
> ∩{E(1), E(2), ..., E(k)} = E(k)
> is a function which remains infinite for all infinite endsegments. If
> all endsegments remain infinite forever, then this function remains
> infinite forever.
It does for all finite k.

-- 
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.