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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Another proof: The Halting Problem Is Undecidable.
Date: Sat, 12 Oct 2024 01:11:40 +0800
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On Fri, 2024-10-11 at 11:42 +0100, Andy Walker wrote:
> On 10/10/2024 16:26, wij wrote:
> > This "0.999...!=3D1" proof [...].
>=20
> 	Any such proof would breach the Archimedean [Eudoxus] axiom, so
> is not a proof about the real numbers.=C2=A0 You have been told that befo=
re.
> If you propose to repeat this or to take it further, you /really, really/
> do need to tell us what axioms you are using instead of those of the real
> numbers.=C2=A0 Without that, your claims, whatever they may be, are worth=
less,
> and no-one qualified to do so can comment more usefully.=C2=A0 WIYF.

Wij's Theorem: x>0 iff x/n >0, where n=E2=88=88=E2=84=A4=E2=81=BA.

Archimedes likely believes that all (real) numbers, including pi, sqrt(2), =
are=20
p/q representable. Is that what you suggest?
Archimedean axiom is an *assertion* that infinitesimal does not exist witho=
ut
knowing the consequence (violating Wij's Theorem which is provable from the=
 rules=C2=A0
stronger than 'assertion').

This is for elementary school students, might help:
https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber2-en.txt/d=
ownload