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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Thu, 10 Apr 2025 02:45:39 +0100
Organization: Fix this later
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On 10/04/2025 01:50, Lawrence D'Oliveiro wrote:
> On Mon, 7 Apr 2025 20:48:27 -0400, Richard Damon wrote:
> 
>> The paper clearly talks about the process continuing indefinitely.
> 
> Note the key point about any computation of a computable number is that
> the answer *converges* to the exact result in the limit. As you compute
> more and more digits, the discrepancy between your approximation and the
> correct answer can be made as close to zero as you like, just as long as
> you don’t ask for it to be zero.
> 
> The Cantor construction does not converge.

It doesn't have to, because computing a number isn't its job. Its 
job is to explain why, no matter how many numbers you have, your 
list is at least one short.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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