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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 1 Dec 2024 11:59:57 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 30 Nov 2024 20:10:49 +0100 schrieb WM:
> On 30.11.2024 18:45, joes wrote:
>> Am Sat, 30 Nov 2024 18:20:51 +0100 schrieb WM:
> 
>>>> 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.
>> True. All endsegments are infinite. But they form a chain of inclusion,
>> and there is no smallest set, because that chain is infinite.
> There is an infinite sequence of endsegments E(1), E(2), E(3), ... and
> an infinite sequence of their intersections E(1), E(1)∩E(2),
> E(1)∩E(2)∩E(3), ... .
> Both are identical - from the first endsegment on until every existing
> endsegment.
How surprising.

>>>>> 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.
>> All natural k are finite.
> Then all endsegments are infinite like their intersections.
....for every natural (which are finite), but not for the limit.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.