Re: Cantor Diagonal Proof

On 04/04/2025 00:18, Lawrence D'Oliveiro wrote:

The Cantor diagonal construction is an algorithm for computing an
incomputable number.

To be more precise, it is an argument, not an algorithm, although it
is a fact that "diagonalisation" as a method has become ubiquitous.
BTW, the argument has indeed been proved constructively: or so they
say, I find that debatable as it needs *extensionality*.

But if there is an algorithm for computing the number, then it is by
definition a computable number.

The anti-diagonal is *as computable as the list is*: and the argument
in fact proves there can be no such list, computable or otherwise...
(no complete list of all such *sequences*: the connection to the real
*numbers* is a further step and problem).
-Julio