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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 03:54:10 -0500
Organization: Peripheral Visions
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WM expressed precisely :
> On 28.11.2024 20:28, FromTheRafters wrote:
>> WM used his keyboard to write :
>>> On 28.11.2024 17:45, joes wrote:
>>>> Am Thu, 28 Nov 2024 11:39:05 +0100 schrieb WM:
>>>
>>>>> A simpler arguments is this: All endsegments are in a decreasing
>>>>> sequence.
>>>> There is no decrease, they are all infinite.
>>>
>>> Every endsegment has one number less than its predecessor.
>>> That is called decrease.
>> 
>> More like the subset relation. It is not a decrease in cardinality.
>
> Of course not. Cardinality is nothing else than infinitely many.

Wrong, it is also 'number of elements' for finite sets.

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