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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Fri, 4 Apr 2025 04:47:13 +0100
Organization: Fix this later
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On 04/04/2025 03:30, Lawrence D'Oliveiro wrote:
> On Fri, 4 Apr 2025 00:49:15 +0100, Richard Heathfield wrote:
> 
>> On 03/04/2025 23:18, 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.
>>
>> I invite you to present an algorithm (a finite sequence of
>> mathematically rigorous instructions) for computing the nth Cantor
>> diagonal.
> 
> Simply repeat the diagonal construction n times.

The diagonal construction starts with a set, and the result you 
get depends on the set you start with, so you end up not with 
/the/ nth Cantor diagonal but one of infinitely many nth Cantor 
diagonals.

The very idea of an "nth" Cantor diagonal is a contradiction.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
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