Re: Cantor Diagonal Proof

On 4/3/25 6:18 PM, Lawrence D'Oliveiro wrote:

The Cantor diagonal construction is an algorithm for computing an
incomputable number.
 But if there is an algorithm for computing the number, then it is by
definition a computable number.

He shows a METHOD to generate that number, but it uses an infinite number of steps, and shows that the number couldn't have been any of the numbers in the original set.
So, if we start with the assumption that the initial set contains EVERY nummber that can be computed, but enumerating EVERY finitely running program that could compute a number, then if there is a number not in that set, that number couldn't have been computed.
"Computing" has the requirement of being finite in steps.