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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: Sat, 30 Nov 2024 13:19:46 +0100
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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.

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.

Regards, WM