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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Fri, 04 Apr 2025 13:37:25 +0800
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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.
>=20
> It is not an algorithm for computing something.=C2=A0 Algorithms are inst=
ructions that operate on finite=20
> inputs and must terminate with an answer at some point for every input.
>=20
> Also, the number defined by the diagonal construction may or may not be c=
omputable, depending on the
> list to which it is applied.=C2=A0 (In the technical sense of "computable=
 numbers" as Turing used the
> term.)
>=20
> =C2=A0=C2=A0 <https://en.wikipedia.org/wiki/Computable_number>
>=20
> Regards,
> Mike.
>=20
> >=20
> > But if there is an algorithm for computing the number, then it is by
> > definition a computable number.
> >=20

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 abou=
t=C2=A0
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.=C2=A0
https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber2-en.txt/d=
ownload
I don't think Cantor's set theory is worth to debunk, so not in my thesis.