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NNTP-Posting-Date: Fri, 04 Apr 2025 16:02:57 +0000
Subject: Re: Cantor Diagonal Proof
Newsgroups: comp.theory
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From: Mike Terry <news.dead.person.stones@darjeeling.plus.com>
Date: Fri, 4 Apr 2025 17:02:57 +0100
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On 04/04/2025 05:22, Lawrence D'Oliveiro wrote:
> On Fri, 4 Apr 2025 04:15:39 +0100, Mike Terry wrote:
> 
>> On 04/04/2025 03:29, Lawrence D'Oliveiro wrote:
>>>
>>> On Fri, 4 Apr 2025 02:41:09 +0100, Mike Terry wrote:
>>>
>>>> On 03/04/2025 23:18, Lawrence D'Oliveiro wrote:
>>>>
>>>>> The Cantor diagonal construction is an algorithm for computing an
>>>>> incomputable number.
>>>>
>>>> It is not an algorithm for computing something.  Algorithms are
>>>> instructions that operate on finite inputs and must terminate with an
>>>> answer at some point for every input.
>>>
>>> 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.
>>>
>> No it doesn't, because for a computable number the algorithm cannot have
>> an infinite amount of input data.
> 
> It doesn’t need to. To compute the Nth digit of the diagonal, it only
> needs N * (N + 1) / 2 digits of the numbers in the first N entries of the
> table.
> 

Yes it does.  The missing number has infinitely many digits, and your attempt to "compute" them 
requires an infinite amount of input data.  That is not a recipe for a computable number!

Mike.