Re: Cantor Diagonal Proof

On 2025-04-10 00:50:10 +0000, Lawrence D'Oliveiro said:

On Mon, 7 Apr 2025 20:48:27 -0400, Richard Damon wrote:
 

The paper clearly talks about the process continuing indefinitely.

 Note the key point about any computation of a computable number is that
the answer *converges* to the exact result in the limit. As you compute
more and more digits, the discrepancy between your approximation and the
correct answer can be made as close to zero as you like, just as long as
you don’t ask for it to be zero.
 The Cantor construction does not converge.

If it is a computable number it does converge. Even if it isn't you may
be able to compute some of the first digits. The more digits you can
compute the coloser to the actual value you can get. But at some point,
perhaps already at the start, there may be a digit you can't compute.
--
Mikko