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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: Mon, 2 Dec 2024 14:52:03 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Mon, 02 Dec 2024 15:28:30 +0100 schrieb WM:
> On 02.12.2024 12:53, FromTheRafters wrote:
> 
>>>> Endsegment E(n) = {n, n+1, n+2, ...}
>> This is his definition of endsegment, which as almost anyone can see,
>> has no last element, so yes it is infinite. He says 'infinite
>> endsegment' as if there were a choice, only to add confusion.
> Infinite endsegments contain an infinite set each
They ARE infinite sets.

> infinitely many elements of which are in the intersection.
The intersection of all infinite segments?

> An empty intersection cannot
> come before an empty endsegment has been produced by losing one element
> at every step.
Which happens only in the limit.

> E(1), E(2), E(3), ...
> and E(1), E(1)∩E(2), E(1)∩E(2)∩E(3), ...
> are identical for every n and in the limit because E(1)∩E(2)∩...∩E(n) =
> E(n).
What do you reckon the limit is?

-- 
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.