Re: Cantor Diagonal Proof

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.  Typically we would have a TM running with a tape containing just the number N finitely encoded somehow and blank elsewhere.
The Cantor diagonal construction takes an infinite list as input...
Mike.