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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Another proof: The Halting Problem Is Undecidable.
Date: Sun, 13 Oct 2024 08:54:34 +0800
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Message-ID: <e7405711e263b0be322ff79f1b58865b7c0c72b0.camel@gmail.com>
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On Sat, 2024-10-12 at 17:16 +0100, Andy Walker wrote:
> On 12/10/2024 02:53, wij wrote:
> > > > Archimedes likely believes that all (real) numbers, including pi, s=
qrt(2), are
> > > > p/q representable. Is that what you suggest?
> > > 	By the time of Archimedes it had been known for several hundred
> > > years that "sqrt(2)" is irrational.
>=20
> 	Established, at the latest, by the Pythagoreans [~500 BCE, nearly 300y
> before Archimedes].=C2=A0 Possibly known earlier. ...
>=20
> > > 					[The status of "pi" remained unknown
> > > for a further ~2K years.]
>=20
> 	First proved by Lambert, in 1761;=C2=A0 1973y after Archimedes died. ...
>=20
> > > 			=C2=A0=C2=A0=C2=A0 =C2=A0 So no, Archimedes did not believe that, =
not
> > > least when he laid some of the foundations of calculus.
>=20
> 	Euclid's "Elements" book 10 is about irrational numbers, and
> Archimedes referred to that book in his writings, so he was certainly
> aware that root(2) is irrational. ...
>=20
> > That is a fabrication (there are many, but... accepted, as a fabricatio=
n)
>=20
> 	... So everything above can be verified by anyone able to google or
> wiki.=C2=A0 Accusing me of lying is not a good way to get the mathematica=
l help
> that you clearly need, esp when the accusation is so clearly false.
>=20
> > > > Archimedean axiom is an *assertion* that infinitesimal does not exi=
st without
> > > > knowing the consequence (violating Wij's Theorem which is provable =
from the rules
> > > > stronger than 'assertion').
> > > 	If "Wij's Theorem" is inconsistent with the axioms of real numbers,
> > > then it is not a theorem of real numbers.=C2=A0 Try one of the other =
systems of
> > > numbers, which you would probably find more to your taste, given the =
other
> > > things you say in this group.
> > Are you kidding? "x>0 iff x/n >0, where n=E2=88=88=E2=84=A4=E2=81=BA" i=
s inconsistent?
>=20
> 	It was /your/ claim that "Wij's Theorem" is "violated" by the
> Archimedean axiom.=C2=A0 /If/ you are right, /then/ your theorem is not t=
rue
> in the standard reals, as used by all numerate scientists and engineers
> and as understood by all mathematicians [even if they /also/ use NSA or
> surreals or other systems].=C2=A0 FWIW, /I/ think your theorem is correct
> in standard analysis, but you seem to object to that.
>=20
> > 								=C2=A0=C2=A0 With your real, yes.=20
> > My real is based on the abacus that can be physically modeled. Tell me,=
 how can
> > it be inconsistent?
>=20
> 	Perhaps you should first explain how you represent infinity and
> infinitesimals on a standard abacus?=C2=A0 "Your" reals can, of course, b=
e
> inconsistent if you insist on axioms that are inconsistent with them.
>=20
> 	[If you persist in insulting those who are trying to help you,
> then you will not get any further reply from me.=C2=A0 I don't intend to =
play
> "Fetch" with you.]

It is I helping you.
"Wij's Theorem" is based on the arithmetic YOU ARE USING NOW.
Archimedean axiom is an purposeful assertion (or just belief without reason=
)

Another example:  If 0.999...=3D p/q =3D1, then 9(9)/10(0)=3Dp/q <=3D> 9(9)=
=3D10(0)
 1. Nominator and denominator are not natural number (find them)
 2. Nominator and denominator are never equal

If 0.999..=3D1, you have to explain your arithmetic system.

If you still believe Modern Pythagoreanism, solve these problems (there are=
 MANY, and NOT BY
ASSERTION)