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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Sat, 5 Apr 2025 00:04:23 +0100
Organization: Fix this later
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On 04/04/2025 22:52, Lawrence D'Oliveiro wrote:
> On Fri, 4 Apr 2025 20:53:31 +0100, Richard Heathfield wrote:
> 
>> On 04/04/2025 20:13, Lawrence D'Oliveiro wrote:
>>
>>> That proof doesn’t quite work, because at any point in the
>>> construction, the number can be shown to match some later item in the
>>> list.
>>
>> Then show it.
> 
> Simple: you have N digits of the supposed-incomputable number so far, and
> there are only B**N (where B is the base of the number system, e.g. 10)
> possible combinations for those digits, compared to an infinite number of
> remaining items in the rest of the list that you haven’t looked at.
> Therefore

Stop right there...

> every possible one of those B**N possibilities will occur
> somewhere in that remaining list.

You have repeated this claim several times, but so far you have 
offered no support in its evidence.

Not all lists are random.

> Therefore the partial number constructed
> so far will always match some later item in the list. QED.

Assumes facts not in evidence.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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