Re: Cantor Diagonal Proof

On Sun, 6 Apr 2025 23:38:25 +0100, Richard Heathfield wrote:

On 06/04/2025 23:01, Lawrence D'Oliveiro wrote:
>

On Sun, 6 Apr 2025 07:53:06 +0100, Richard Heathfield wrote:
 

After infinitely many steps ...

 
I.e. never.

 
If you mean you can never know all the digits, hey, you're right.
No algorithm can derive the number. It's incomputable.

That’s not what “incomputable” means.

But "never" is a strong word.

Like anything in mathematics, you need proof before claiming something.

This is why we have proof-by-induction: it’s essentially the only way to
make generalized statements about infinite sequences. Instead of an
infinite number of propositions to be proved, it boils the whole lot down
to two:

    P(1)
    P(N) ⊢ P(N + 1)

I gave my proof-by-induction; it is up to you to try to tear it down. If
you can.