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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: Sun, 8 Dec 2024 11:59:24 +0100
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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.
> 
>>> 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?

Regards, WM