Sujet : Re: Cantor Diagonal Proof
De : ldo (at) *nospam* nz.invalid (Lawrence D'Oliveiro)
Groupes : comp.theoryDate : 04. Apr 2025, 08:21:36
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vso1a0$2sf7o$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Pan/0.162 (Pokrosvk)
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. Therefore there is
guaranteed to be some number we haven’t looked at yet with all those first
N digits the same.
…