Sujet : Re: Cantor Diagonal Proof
De : wyniijj5 (at) *nospam* gmail.com (wij)
Groupes : comp.theoryDate : 04. Apr 2025, 06:37:25
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <2318243ce57284ba469fcbf7270590c9e65929c3.camel@gmail.com>
References : 1 2
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On Fri, 2025-04-04 at 02:41 +0100, Mike Terry wrote:
On 03/04/2025 23:18, Lawrence D'Oliveiro wrote:
The Cantor diagonal construction is an algorithm for computing an
incomputable number.
It is not an algorithm for computing something. Algorithms are instructions that operate on finite
inputs and must terminate with an answer at some point for every input.
Also, the number defined by the diagonal construction may or may not be computable, depending on the
list to which it is applied. (In the technical sense of "computable numbers" as Turing used the
term.)
<https://en.wikipedia.org/wiki/Computable_number>
Regards,
Mike.
But if there is an algorithm for computing the number, then it is by
definition a computable number.
If we say the 'real number' in the diagonal construction is rational number, it
will also fits the description.
The author of the wiki (maybe the same as Cantor) was actually talking about
rational number but think they are talking about real number.
There are many 'magic', too, in Cantor's set theory.
The basic idea of infinity is very simple.
https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber2-en.txt/downloadI don't think Cantor's set theory is worth to debunk, so not in my thesis.
Cantor Diagonal Proof
Re: Cantor Diagonal Proof