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From: Lawrence D'Oliveiro <ldo@nz.invalid>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Thu, 10 Apr 2025 00:41:03 -0000 (UTC)
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On Tue, 8 Apr 2025 18:57:17 -0400, Richard Damon wrote:

> On 4/8/25 5:02 PM, Lawrence D'Oliveiro wrote:
>>
>> On Mon, 7 Apr 2025 18:24:36 -0400, Richard Damon wrote:
>> 
>>> And that is because while every element on the list has an algorithm
>>> to construct it, that list is infinite, so you can't just put them
>>> *ALL* in to one finite algorithm to compute any one you need at the
>>> moment.
>> 
>> But that’s exactly how computable numbers work.
> 
> No, *A* computable number has a finite algorithm that computes it.
> Finite in having finite instructions in its algorithm and finite states
> to process.
> 
> The problem is your "master" algorithm need the algorithms of *ALL* the
> computable numbers within it, which is an infinite number of algorithms,
> and thus isn't itself a finite algorithm.

That is the problem with the Cantor construction, not with my disproof of 
it. My disproof of it only needs a finite number of list elements at any 
point in the proof. The Cantor construction needs them all.