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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Mon, 2 Dec 2024 08:39:32 +0100
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Am 02.12.2024 um 00:11 schrieb Chris M. Thomasson:
> On 11/30/2024 3:12 AM, WM wrote:

FINSON(s)

>> Finite initial segment[s]: F(n) = {1, 2, 3, ..., n}   (n e IN)

You see it's a DEFINITION:

         F(n) = {1, 2, 3, ..., n}   (n e IN) .

This "means" (implies): F(1) is a FISON (i.e. {1}), F(2) is a FISON 
(i.e. {1, 2}), F(3) is a FISION (i.e. {1, 2, 3}), and so on (ad 
infinitum). F(1), F(2), F(3), ... are FISONs.

> Finite? 

Yeah, finite. For each and eveer n e IN F(n) (i.e. {1, 2, 3, ..., n}) is 
finite (i.e. a finite set).

Huh? The natural numbers don't stop at n! WTF!!!

No one (except possibly Mückenheim) said they did.

Hint: There are _infinitely many_ finite initial segments (one for each 
and every natural number n). :-)