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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sat, 23 Nov 2024 09:54:36 +0100
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On 22.11.2024 23:56, Jim Burns wrote:
> On 11/22/2024 4:30 PM, WM wrote:

>> Remember:
>> The intersection of all endsegments is empty,
>> but the intersection of
>> endsegments which can be counted to
>> is infinite.
> 
> No one should "remember" that.
> It is incorrect.

∀k ∈ ℕ_def: ∩{E(1), E(2), ..., E(k)} = E(k), |E(k)| = ℵ₀
∩{E(1), E(2), ...} = { }.
> 
>> Note that every endsegment loses only one number.
> 
> Finite cardinalities can lose one number.

For all endsegments:
∀k ∈ ℕ: |E(k+1)| = |E(k)| - 1

>> Therefore there must
>> exist infinitely many finite endsegments.

Regards, WM