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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Mon, 7 Apr 2025 23:45:19 +0100
Organization: Fix this later
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On 07/04/2025 22:42, Lawrence D'Oliveiro wrote:
> On Mon, 7 Apr 2025 02:10:23 -0600, Jeff Barnett wrote:
> 
>> You are quite wrong about an elementary proof and various of your
>> misunderstandings have been pointed out to you ...
> 
> I gave a proof by induction why the Cantor construction fails on that
> flipped-integer list; no one has yet pointed out a flaw in that proof.

I've already pointed out the flaw, which is that it ignores the 
Cantor diagonal argument. Cantor's construction differs by at 
least one digit from every element in the list.

> Somebody kept insisting that, even if my proposition is true for every
> element in the list,

That is, even if you are building the number one digit at a time 
and the number constructed to date appears later on in the list...

> it somehow goes false at the end. The end of an
> infinite list! Yeah, right.

Yeah, right - it fails when you hit infinity. When Achilles 
catches the tortoise, the complete Cantor construction differs 
from /every/ number in the list by at least one digit.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within