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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Mon, 07 Apr 2025 18:31:28 +0800
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In-Reply-To: <vt02b9$3abfr$1@dont-email.me>

On Mon, 2025-04-07 at 11:28 +0300, Mikko wrote:
> On 2025-04-06 10:42:05 +0000, wij said:
>=20
> > On Sun, 2025-04-06 at 13:35 +0300, Mikko wrote:
> > > On 2025-04-06 07:15:51 +0000, wij said:
> > >=20
> > > > On Sun, 2025-04-06 at 06:43 +0000, Lawrence D'Oliveiro wrote:
> > > > > On Sun, 6 Apr 2025 07:27:43 +0100, Richard Heathfield wrote:
> > > > >=20
> > > > > > On 06/04/2025 06:40, Lawrence D'Oliveiro wrote:
> > > > > >=20
> > > > > > > On Sat, 5 Apr 2025 09:07:22 +0100, Richard Heathfield wrote:
> > > > > > >=20
> > > > > > > > But to be computable, numbers must be computed in a finite =
number of
> > > > > > > > steps.
> > > > > > >=20
> > > > > > > =E2=80=9CComputable Number: A number which can be computed to=
 any number of
> > > > > > > digits desired by a Turing machine.=E2=80=9D
> > > > > > >=20
> > > > > > > <https://mathworld.wolfram.com/ComputableNumber.html>
> > > > > >=20
> > > > > > "The =E2=80=9Ccomputable=E2=80=9D numbers may be described brie=
fly as the real numbers
> > > > > > whose expressions as a decimal are calculable by finite means."=
 - Alan
> > > > > > Turing.
> > > > > >=20
> > > > > > And therefore, to be computable, numbers must be computed in a =
finite
> > > > > > number of steps.
> > > > >=20
> > > > > I would say you are quoting Turing out of context. By your>> > >=
=20
> > > > > (mis)interpretation of his words, even something like 1/3 is an>>=
 > >=20
> > > > > incomputable number, since its =E2=80=9Cexpressions as a decimal =
are not>> > >=20
> > > > > calculable by finite means=E2=80=9D.
> > > >=20
> > > > Simply put, repeating decimals are irrational.
> > > > https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber2-=
en.txt/download=C2=A0
> > > >=20
> > > >=20
> > >=20
> > > Repeating decimals are rational.
> >=20
> > Prove it (be sure not to make mistakes shown in the link above)
>=20
> See=20
> https://math.stackexchange.com/questions/549254/why-is-a-repeating-decima=
l-a-rational-number=C2=A0
>=20

Still can't prove, except posting a copy from the internet?