Re: Cantor Diagonal Proof

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
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