Cantor Confusion
in [Math]
|
Prev: Pi berechnen: Ramanujan oder BBP
Next: Group Theory
From: David Marcus on 4 Nov 2006 14:28 Lester Zick wrote: > On Fri, 3 Nov 2006 17:19:15 -0500, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > >Lester Zick wrote: > >> On Thu, 2 Nov 2006 18:57:30 -0500, David Marcus > >> <DavidMarcus(a)alumdotmit.edu> wrote: > >> >Virgil wrote: > >> >> WM merely repeated his automatic error several more times here. > >> >> > >> >> WM claims that a list in which the nth listed element is a string of > >> >> length at least n characters cannot produce a diagonal of length > >> >> greater that any finite number of characters. > >> >> > >> >> His claim is trivially and obviously false, but he keeps repeating it ad > >> >> nauseam, as if by sufficient repetition of that lie , he can make the > >> >> truth go away. > >> > > >> >Not only does he keep repeating it, but he never even tries to justify > >> >it in any way. He is like a broken record. We ask him for his reason and > >> >he just repeats the same unjustified, erroneous claim. Kind of boring. > >> > >> No more boring than endless repetition of "true" "infinity" "set > >> theory" and "bijection". Kinda grates on the nerves. Repetition and > >> truth just don't converge. > > > >Are you referring to your own posts? > > I'm referring to the posts of those who biject set theory with truth. So, you are referring to no one? -- David Marcus
From: Virgil on 4 Nov 2006 15:48 In article <1162643826.959162.135860(a)h48g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > MoeBlee schrieb: > > > As > > to set theory, for the tenth time: Without the axiom of infinity it is > > UNDETERMINED whether every set is finite. > > For the eleventh time: Infinity is NOWHERE. That is where Meuckenheim is, so he should have a good view of infinity. Surprising that he does not see it. > To assume the existence of > actual infinity is one of the greatest errors of human mind. To assume that one can imagine what one has imagined is scarcely erroneous. The error is to imagine that one cannot imagine what one has imagined. And that is the error Meickenh makes. > Therefore, > without explicitly assuming this notion, it cannot be anywhere. It is, as is all of mathematics, only in the mind. > > > > > Whatever your point, you won't be able to show that merely dropping the > > axiom of infinity from the Z axioms entails that there are only finite > > sets. > > Whatever your point, you won't be able to show that merely dropping the > axiom of rabbithood from the Z axioms entails that there are only > non-rabbit > sets. Which axiom of ZF or NBG does WM connect with rabbits? > To put it in other words: It simply an imbecile nonsense to talk about > finished infinity without explicitly stating that it was not. The only imbicile here is WM himself, attempting to dictate to others what they are allowed to think. > > > > Modern set theory simply cannot describe developing sets as > > > it apparently cannot describe sets with limited contents of > > > information. > > > > Whatever your definition of "developing sets" and 'limited contents of > > information", the fact remains that dropping the axiom of infinity does > > NOT entail that there are no infinite sets. > > > > > These things are unknown to the slaves of formalism. Read a good book > > > like Fraenkel, Abraham A., Bar-Hillel, Yehoshua, Levy, Azriel: > > > "Foundations of Set Theory", North Holland, Amsterdam (1984). There you > > > will find more about that topic. > > > > Oh please, I've read more in that book than you have. > > That is strange. I read all of it, but you read more. This simple > sentence alone would prove that you must be a set-theorist. Because set therists are capable or getting more out of books thtan WM is? That puts WM on a par with my grandson who cannot yet read at all, though in my grandson's case that will change soon. > > Regards, WM
From: Virgil on 4 Nov 2006 15:55 In article <1162644069.367117.114880(a)h54g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > MoeBlee schrieb: > > > > For ordinals, > > > > x<y <-> xey > > > > where 'e' is the epsilon membership symbol. > > That is identical with my definition. Take for instance Zermelo's > definition of the naturals or Cantor's own (Collected works, p. > 289-290), then you can see it. Your definition has been simply > translated from Cantor's. Please don't conclude from your own ignorance > on mine. > > > > > If it cannot be a fraction because ZF does > > > not yet know how to divide elements, > > > > In ZF we define various operations of division. As far as I know, there > > is not a dvision operation for sets in general. > > Why then do you not understand how an edge of the binary tree can be > divided? But once divided, the parts are no longer edges at all, so are useless. What I cannot understand is when trying to estatblish a correspondece between undivided edges and undivided paths, what relevance dividing up either might have. > > > > These problems you're having are of fitting set theory to your own > > system of terminology. To work in set theory, we don't need to care > > about your own system of terminology. > > "Whole number" is not my terminology. It is certainly not that of anyone else here, and since you brought it in, it is yours. > Please don't conclude from your own ignorance on mine. We don't. WM has a wholly different and larger form of ignorance, of the sort sometimes denoted as "invincible ignorance".
From: Lester Zick on 4 Nov 2006 17:44 On Sat, 4 Nov 2006 14:28:28 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Lester Zick wrote: >> On Fri, 3 Nov 2006 17:19:15 -0500, David Marcus >> <DavidMarcus(a)alumdotmit.edu> wrote: >> >Lester Zick wrote: >> >> On Thu, 2 Nov 2006 18:57:30 -0500, David Marcus >> >> <DavidMarcus(a)alumdotmit.edu> wrote: >> >> >Virgil wrote: > >> >> >> WM merely repeated his automatic error several more times here. >> >> >> >> >> >> WM claims that a list in which the nth listed element is a string of >> >> >> length at least n characters cannot produce a diagonal of length >> >> >> greater that any finite number of characters. >> >> >> >> >> >> His claim is trivially and obviously false, but he keeps repeating it ad >> >> >> nauseam, as if by sufficient repetition of that lie , he can make the >> >> >> truth go away. >> >> > >> >> >Not only does he keep repeating it, but he never even tries to justify >> >> >it in any way. He is like a broken record. We ask him for his reason and >> >> >he just repeats the same unjustified, erroneous claim. Kind of boring. >> >> >> >> No more boring than endless repetition of "true" "infinity" "set >> >> theory" and "bijection". Kinda grates on the nerves. Repetition and >> >> truth just don't converge. >> > >> >Are you referring to your own posts? >> >> I'm referring to the posts of those who biject set theory with truth. > >So, you are referring to no one? Not especially. ~v~~
From: Lester Zick on 4 Nov 2006 17:45
On Sat, 4 Nov 2006 11:59:25 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >mueckenh(a)rz.fh-augsburg.de wrote: >> MoeBlee schrieb: >> >> > As >> > to set theory, for the tenth time: Without the axiom of infinity it is >> > UNDETERMINED whether every set is finite. >> >> For the eleventh time: Infinity is NOWHERE. To assume the existence of >> actual infinity is one of the greatest errors of human mind. Therefore, >> without explicitly assuming this notion, it cannot be anywhere. > >Moe was discussing axiomatic set theory, specifically ZF without the >axiom of infinity. You clearly are discussing philosophy, e.g., >"greatest errors of the human mind". If you wish to discuss philosophy, >feel free, but please do not inject philosophy into a discussion of >mathematics without saying you are doing so. So what's the difference exactly between what Moe was discussing and philosophy? ~v~~ |