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From: Lawrence D'Oliveiro <ldo@nz.invalid>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Fri, 11 Apr 2025 00:29:56 -0000 (UTC)
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On Thu, 10 Apr 2025 10:37:49 +0300, Mikko wrote:

> On 2025-04-10 00:50:10 +0000, Lawrence D'Oliveiro said:
> 
>> 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.
> 
> If it is a computable number it does converge.

That’s a key point of my proof: if it converges, then the number is 
already in the list. The only way it can come up with a number not in the 
list is by never converging.