Re: Cantor Diagonal Proof

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.