Sujet : Re: Cantor Diagonal Proof
De : rjh (at) *nospam* cpax.org.uk (Richard Heathfield)
Groupes : comp.theoryDate : 07. Apr 2025, 09:21:25
Autres entêtes
Organisation : Fix this later
Message-ID : <vt01u5$38f07$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
User-Agent : Mozilla Thunderbird
On 07/04/2025 08:33, Lawrence D'Oliveiro wrote:
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:
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After infinitely many steps ...
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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.
Yeah, it is. We've already had this argument. Turing won: "The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by finite means."
But "never" is a strong word.
Like anything in mathematics, you need proof before claiming something.
Like anything in mathematics, if you're going to overturn a long-established proof you're going to need a better argument than that you don't understand what it proves.
This is why we have proof-by-induction: it’s essentially the only way to
make generalized statements about infinite sequences.
No, it's not. Take Cantor's diagonal argument, for example.
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.
No, it isn't. The mathematical world already agrees with me (or rather, I agree with it), so I don't have to do spit. You, on the other hand, have your work cut out.
-- Richard HeathfieldEmail: rjh at cpax dot org dot uk"Usenet is a strange place" - dmr 29 July 1999Sig line 4 vacant - apply within
Cantor Diagonal Proof
Re: Cantor Diagonal Proof