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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, 14 Dec 2024 12:21:28 +0100
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On 14.12.2024 12:00, joes wrote:
> Am Sun, 08 Dec 2024 11:55:34 +0100 schrieb WM:
>> On 08.12.2024 11:43, joes wrote:
>>> Am Sat, 07 Dec 2024 22:50:27 +0100 schrieb WM:
>>
>>>> ∀n ∈ ℕ: E(1)∩E(2)∩...∩E(n) = E(n)
>>>> All n are infinitely many.
>>> That sentence only talks about a single n at a time, though,
>>> not about the infinite intersection.
>> It talks about all n and therefore about all E(n).
> No, it says nothing about the intersection of all E(n),
> only about finite intersections

All E(n) have finite indices n. But the quantifier-nonsense is no longer 
under discussion because the intersections are sufficient and accepted 
as becoming empty. And their procedure is the same as that of the 
endsegments:
∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k}).

Regards, WM