Re: Cantor Diagonal Proof

On 4/10/25 8:30 PM, Lawrence D'Oliveiro wrote:

On Wed, 9 Apr 2025 22:00:15 -0400, Richard Damon wrote:
 

The problem with the "Cantor Construction" is that one of the steps,
"Compute to the Nth digit of the Nth number" isn't computable with a
finite algorithm.

 But N is always finite, therefore the construction is always finite.

N my be finite, but is unbounded, and thus the construction is unbounded in size, and thus not finite.
This is the issue with talking about these things, something true for ALL N, is talking about an infinite set, and thus is talking about infinite things, and thus isn't finite.