Re: Cantor Diagonal Proof

On 04/04/2025 08:21, Lawrence D'Oliveiro wrote:

On Fri, 4 Apr 2025 07:24:35 +0100, Richard Heathfield wrote:
 

On 04/04/2025 07:15, Lawrence D'Oliveiro wrote:
>

On Fri, 4 Apr 2025 06:16:20 +0100, Richard Heathfield wrote:
>

The Cantor diagonal argument shows that *any* list, finite or
infinite,
is incomplete.

>
But it takes an infinite number of steps to show that for an infinite
list. And at every point, the probability that the N digits computed so
far match some number later in the list is 1.

>
Depends on the list.

 No it doesn’t. At every point N, we have the first N digits of our
hypothetical number-that-is-not-in-the-list. But we have an infinitude of
remaining numbers in the list we haven’t looked at, among which all
possible combinations of those N digits will occur.

Show me your first N digits, and I'll show you a counterexample.

Therefore there is
guaranteed to be some number we haven’t looked at yet with all those first
N digits the same.

And yet you still won't post those first N digits. It's almost like you already know that as soon as you do I'll be able to post a counterexample, so you have to keep stalling.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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