Re: Cantor Diagonal Proof

On Fri, 4 Apr 2025 04:15:39 +0100, Mike Terry wrote:

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.

It doesn’t need to. To compute the Nth digit of the diagonal, it only
needs N * (N + 1) / 2 digits of the numbers in the first N entries of the
table.