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From: Lawrence D'Oliveiro <ldo@nz.invalid>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Fri, 4 Apr 2025 02:31:14 -0000 (UTC)
Organization: A noiseless patient Spider
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On Thu, 3 Apr 2025 18:50:08 -0400, Richard Damon wrote:

> On 4/3/25 6:18 PM, Lawrence D'Oliveiro wrote:
>>
>> The Cantor diagonal construction is an algorithm for computing an
>> incomputable number.
>> 
>> But if there is an algorithm for computing the number, then it is by
>> definition a computable number.
> 
> He shows a METHOD to generate that number, but it uses an infinite
> number of steps, and shows that the number couldn't have been any of the
> numbers in the original set.

The definition of a “computable number” is that for any integer N, there 
is an algorithm that will compute digit N of the number in a finite 
sequence of steps.

Does the Cantor diagonal construction fit this definition? Yes it does.