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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail 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 Organization: A noiseless patient Spider Lines: 86 Message-ID: <e7405711e263b0be322ff79f1b58865b7c0c72b0.camel@gmail.com> References: <789da1c7da825d24f5298891efae209a44535ca5.camel@gmail.com> <0cf5c2dd4c7f1042c1d52ea45a30847ea4bc3e38.camel@gmail.com> <veaved$3jher$1@dont-email.me> <bd415cc46f2a87bb642028be2e99b999e8c7c6fd.camel@gmail.com> <vec20n$3jher$3@dont-email.me> <9810f381018797df92f66066e96a63386071658b.camel@gmail.com> <vee7dm$3ja6$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Injection-Date: Sun, 13 Oct 2024 02:54:36 +0200 (CEST) Injection-Info: dont-email.me; posting-host="e7eb51d7b8f96eb9f93f67d9627a30ab"; logging-data="408247"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/PxQX0f4ZSkPJXIfle3m+T" User-Agent: Evolution 3.50.2 (3.50.2-1.fc39) Cancel-Lock: sha1:FqDURUf/5oYbuyYJu+pSYDHwaI8= In-Reply-To: <vee7dm$3ja6$1@dont-email.me> Bytes: 4802 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)