Re: Cantor Diagonal Proof

On 4/9/25 8:41 PM, Lawrence D'Oliveiro wrote:

On Tue, 8 Apr 2025 18:57:17 -0400, Richard Damon wrote:
 

On 4/8/25 5:02 PM, Lawrence D'Oliveiro wrote:

>
On Mon, 7 Apr 2025 18:24:36 -0400, Richard Damon wrote:
>

And that is because while every element on the list has an algorithm
to construct it, that list is infinite, so you can't just put them
*ALL* in to one finite algorithm to compute any one you need at the
moment.

>
But that’s exactly how computable numbers work.

>
No, *A* computable number has a finite algorithm that computes it.
Finite in having finite instructions in its algorithm and finite states
to process.
>
The problem is your "master" algorithm need the algorithms of *ALL* the
computable numbers within it, which is an infinite number of algorithms,
and thus isn't itself a finite algorithm.

 That is the problem with the Cantor construction, not with my disproof of
it. My disproof of it only needs a finite number of list elements at any
point in the proof. The Cantor construction needs them all.

But a finite list can't get you to the needed arbitrary precision needed.
Not also, Cantor only claimed that the numbers weren't countable, he didn't talk about computable. That is a later work looking at the proof.