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From: Lawrence D'Oliveiro <ldo@nz.invalid>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Fri, 4 Apr 2025 21:52:06 -0000 (UTC)
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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 every possible one of those B**N possibilities will occur 
somewhere in that remaining list. Therefore the partial number constructed 
so far will always match some later item in the list. QED.