Cantor Confusion
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From: David Marcus on 7 Feb 2007 00:14 Federico Ferreres Solana wrote: > Call me ignorant, but I don't understand what Cantor is trying to do with the diagonal. > > FRACT --> NATURALS > 0.0 --> 0 > 0.1 --> 1 > 0.2 --> 2 > 0.3 --> 3 > .. --> ... > 0.9 --> 9 > 0.01 --> 10 > 0.11 --> 11 > 0.12 --> 12 > (etc) > > This uses the same properties than his (or whoever did that) > mapping of rationals to naturals, and would cover all fractional > numbers. If you don't like the mapping rule (function, operation > or whatever)...call it self referential, not an operation...who > cares? Each and every fractional has natural associated with it, > and no more. Dilbert is happy. If you think not, then show me a > number (if it's infinitely large as PI-3, I will of course express > it as REVERSE(PI-3), And, of course, that's not a natural number. Are you trolling or a crank? -- David Marcus
From: G. Frege on 7 Feb 2007 02:33 On Wed, 7 Feb 2007 00:14:16 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > Federico Ferreres Solana wrote: >> >> Call me ignorant, but I don't understand what Cantor is trying to do >> with the diagonal. >> Obviously. :-) >> >> FRACT --> NATURALS >> 0.0 --> 0 >> 0.1 --> 1 >> 0.2 --> 2 >> 0.3 --> 3 >> .. --> ... >> 0.9 --> 9 >> 0.01 --> 10 >> 0.11 --> 11 >> 0.12 --> 12 >> (etc) >> >> This uses the same properties than his (or whoever did that) >> mapping of rationals to naturals, and would cover all fractional >> numbers. If you don't like the mapping rule (function, operation >> or whatever)...call it self referential, not an operation...who >> cares? Each and every fractional has natural associated with it, >> and no more. Dilbert is happy. If you think not, then show me a >> number (if it's infinitely large as PI-3, I will of course express >> it as REVERSE(PI-3), >> > And, of course, that's not a natural number. > > Are you trolling or a crank? > That'S for sure: The set of cranks is uncountable! :-) F. -- E-mail: info<at>simple-line<dot>de
From: G. Frege on 7 Feb 2007 02:46 On Wed, 7 Feb 2007 01:52:19 GMT, "Dik T. Winter" <Dik.Winter(a)cwi.nl> wrote: >> >> "3 is the set of all sets of 3 elements." >> > ...that is a ridiculous definition, as that is extremely circular. > He could avoid that by claiming: 3 is the set of all sets equinumberous to the set {0,1,2}. (Of course we could not use this definition in ZFC.) I guess that's what he _meant_. Let's face it: WM is a complete idiot if it comes to _mathematics_. F. -- E-mail: info<at>simple-line<dot>de
From: mueckenh on 7 Feb 2007 07:31 On 6 Feb., 11:42, Franziska Neugebauer <Franziska- Neugeba...(a)neugeb.dnsalias.net> wrote: > mueck...(a)rz.fh-augsburg.de wrote: > > On 6 Feb., 11:22, Franziska Neugebauer <Franziska- > > Neugeba...(a)neugeb.dnsalias.net> wrote: > >> mueck...(a)rz.fh-augsburg.de wrote: > >> > Franziska Neugebauer wrote: > >> [...] > >> >> > The simplest reason is that omega - n = omega for all n in N. > > >> >> Where did you get that from? Reference? EB? > > >> > You could even figure it out by yourself. > > >> I cannot find any reference. Perhaps, there is none. > > > Already Cantor knew it, but I am too lazy to look for the reference. > > Read his papers, then you will encounter it. > > You are certainly able to brief a proof of "omega - n = omega for all n > in N.", are you? And of course to define subtraction involving > non-natural numbers like omega. Was soll die Aufregung, meine Dame? Wer in der Küche kochen will, muß Hitze vertragen. Wer Unsinn als Zahl verkaufen will, darf sich nicht wundern, wenn der Zahlcharakter auch geprüft wird Cantor, Collected Works p. 323: Es kommt hier noch die Operation der Subtraktion hinzu. Sind a und b zwei Ordnungszahlen und a < b, so existiert immer eine bestimmte Ordnungszahl, die wir b - a nennen ... Ist omega eine Ordnungszahl > n für jede natürliche Zahl n? Gruß, WM
From: mueckenh on 7 Feb 2007 07:33
On 6 Feb., 13:21, Franziska Neugebauer <Franziska- Neugeba...(a)neugeb.dnsalias.net> wrote: > mueck...(a)rz.fh-augsburg.de wrote: > > On 5 Feb., 05:10, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > [...] > > > Of course the requirement to decide whether n is in N is more circular > > than the statement that 1 is in N. > > Contemporary set theories do not have these kind of problems. > > [...] > > >> it is impossible to talk about > >> it, at least mathematically. > > > Present mathematics has nothing in common with existence. > > In present mathematics "existence" does not mean *physical* existence. In present mathematics "existence" is meaningless. > > [...] > > >> Existence is a mathematical thing when you can establish it by axioms > >> or through theorems based on axioms. Anything else is merely > >> phylosophy. > > > There is something called reality and another thing called matheology. > > The latter is taught in Augsburg. No. That is a wrong statement. But typical for an advocate of finished infinity. Regards, WM |