Sujet : Re: Cantor Diagonal Proof
De : julio (at) *nospam* diegidio.name (Julio Di Egidio)
Groupes : comp.theoryDate : 04. Apr 2025, 12:47:29
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vsogsi$38bb3$1@dont-email.me>
References : 1
User-Agent : Mozilla Thunderbird
On 04/04/2025 00:18, Lawrence D'Oliveiro wrote:
The Cantor diagonal construction is an algorithm for computing an
incomputable number.
To be more precise, it is an argument, not an algorithm, although it
is a fact that "diagonalisation" as a method has become ubiquitous.
BTW, the argument has indeed been proved constructively: or so they
say, I find that debatable as it needs *extensionality*.
But if there is an algorithm for computing the number, then it is by
definition a computable number.
The anti-diagonal is *as computable as the list is*: and the argument
in fact proves there can be no such list, computable or otherwise...
(no complete list of all such *sequences*: the connection to the real
*numbers* is a further step and problem).
-Julio