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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: Fri, 29 Nov 2024 07:23:55 -0500
Organization: Peripheral Visions
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WM was thinking very hard :
> 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.

Your sequence of endsegments (which are each countably infinte) is 
indeed losing an element of N with each iteration. Losing an element is 
not the same as reducing an infinite set's size though.