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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: Fri, 29 Nov 2024 11:57:13 +0100
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On 29.11.2024 09:54, FromTheRafters wrote:
> WM expressed precisely :

>> But as long as infinitely many natnumbers have not left the 
>> endsegments, they stay inside all of them. And many are the same for 
>> all endsegments. Therefore the intersection of infinite endsegments is 
>> infinite.
> 
> Natural numbers don't "leave", sets don't change.

Call it as you like. Fact is that the function of endsegments is losing 
elements. The limit is the empty endsegment.

> You don't 'run out of 
> indices' or elements to index.

As long as infinitely many natnumbers are within endsegments, there are 
only finitely many indexed endsegments. All endsegments containing 
infinitely many natnumbers are finitely many.

Regards, WM