Re: Cantor Diagonal Proof

On 04/04/2025 06:00, Lawrence D'Oliveiro wrote:

On Fri, 4 Apr 2025 05:46:46 +0100, Richard Heathfield wrote:
 

On 04/04/2025 05:24, Lawrence D'Oliveiro wrote:
>

At every point, the probability that the N digits computed so far match
some number later in the list is 1.

>
Counter-example follows.
>
Input list:
>
1111
2222
3333
4444

 Is that all? Just 4 numbers?

The Cantor diagonal argument shows that *any* list, finite or infinite, is incomplete. If you would prefer to illustrate your point using an infinite list that's fine by me, but even at 100Mbps it's going to take a while to upload to your news server.
If you do go for an infinite list, bear in mind that there are infinitely many infinite lists. For every set of N digits you can construct such that "at every point, the probability that the N digits computed so far match some number later in the list is 1", I can define an infinite list that doesn't contain it.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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