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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 20:33:16 +0100
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On 29.11.2024 13:23, FromTheRafters wrote:
> 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.

The size of the intersection remains infinite as long as all endsegments 
remain infinite (= as long as only infinite endsegments are considered).

Regards, WM