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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 18:20:51 +0100
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On 30.11.2024 16:58, joes wrote:
> Am Sat, 30 Nov 2024 13:19:46 +0100 schrieb WM:
>> 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.
> For an intersection, the "smallest" set matters, which there isn't
> in this infinite sequence, only a "biggest".

If all sets are infinite, then there is no smaller set than an infinite set.
> 
>> 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.
> It does for all finite k.

Of course. Only for finite k the endsegments are infinite.

Regards, WM
>