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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, 9 Dec 2024 19:48:10 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sun, 08 Dec 2024 11:59:24 +0100 schrieb WM:
> On 08.12.2024 11:46, joes wrote:
>> Am Sat, 07 Dec 2024 22:37:04 +0100 schrieb WM:
> 
>>> ∀n ∈ ℕ: E(1)∩E(2)∩...∩E(n) = E(n).
>>> Every counter argument has to violate this. That is inacceptable.
>> Incorrect. "More than finite" means infinite. Your formula only talks
>> about finite intersections.
> It talks about all finite intersections.
And not about the infinite intersection.

>>>> Each finite.cardinality cannot be more.than.finitely.many
>>> So it is. Each finite cardinal cannot turn a finite set into an
>>> infinite set. But even for infinite sets we have ∀n ∈ ℕ:
>>> E(1)∩E(2)∩...∩E(n) = E(n).
>> That is not an infinite intersection.
> It is the sequence of all endsegments and of all finite intersections.
> The limits of identical sequences are identical
>>> ∀n ∈ ℕ: E(1)∩E(2)∩...∩E(n) = E(n).
>>> No empty intersection without an empty endsegment.
>> That happens, as you know, only in the limit.
> And what is the limit?
Empty, like you said.

-- 
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.