Re: Cantor Diagonal Proof

On 4/8/25 5:05 PM, Lawrence D'Oliveiro wrote:

On Mon, 7 Apr 2025 06:47:43 -0400, Richard Damon wrote:
 

And an infinite listing of values doesn't need to be computable, even if
every number in the list is computable.

 Computability is a characteristic of particular numbers. It is a
characteristic of all the numbers in the list, and of the number that the
Cantor construction tries to construct from those numbers in the list.
 The fact that you can’t apply that characteristic to the set as a whole is
irrelevant, since the set itself is not a number.

Right, so the DIAGONAL number, which you claim to be computable, needs a finite algorithm to do so.
The algorithm described is NOT FINITE, as it includes the infinite number of algorithms to compute all the other numbers.
The problem is the list of numbers it is using is infinite, so the list of algorithms is also, so can't be held in a finite algorithm.