Cantor Confusion
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From: David Marcus on 24 Oct 2006 22:06 georgie wrote: > David Marcus wrote: > > georgie wrote: > > > David Marcus wrote: > > > > georgie wrote: > > > > The OP said that a definition was invalid because it was self- > > > > referential. However, there is no rule against self-reference in modern > > > > mathematics, so the OP's objection is not valid. > > > > > > So the set of sets containing themselves is ok by you. > > > > I don't see where I said that. I said there is no rule against self- > > reference. The rules are specified by the axioms of ZFC. > > So it's valid or it isn't and it's only valid when you like it. Is > that your position. From your reactions it appears that way. If you don't > explain why you think self-reference is ok in some cases and not others, you > lose credibility. Please read what I wrote: The rules are specified by the axioms of ZFC. In other words, the axioms tell you when it is allowed. If you take some math classes or read some books, you could learn the rules. -- David Marcus
From: David Marcus on 24 Oct 2006 22:08 Han de Bruijn wrote: > David Marcus wrote: > > You mean all the cranks think they understand it. If they really > > understood it (and it made sense--a rather big assumption that), they > > could explain it in standard language. It isn't even that much fun to > > banter with Mueckenheim because so little of what he says is even > > understandable. > > Haha! What you say about Bohmian mechanics is understandable for anyone > who has studied Newtonian mechanics. But it's nevertheless outdated. As > one of your "cranks", I am at least up to date as Quantum Mechanics and > Relativity are concerned. But you can not say such a thing. So who is a > "crank" in this debate? Clearly, you are the crank. Once a crank, always a crank. I have no idea why you are comparing Newtonian Mechanics and Bohmian Mechanics, the two are about as far apart as you can get. -- David Marcus
From: David Marcus on 24 Oct 2006 22:10 Han de Bruijn wrote: > David Marcus wrote: > > Han de Bruijn wrote: > >>And no, binary trees will not be found in Halmos' "Naive Set Theory". > >>Because it's too naive, I suppose .. > > > > I don't see how you would know it is not there since you said that while > > you own the book, you've never read it. Funny how books aren't much use > > if you don't actually read them. > > > > Anyway, I didn't say binary trees were in the book. I said that if > > Muckenheim wants to talk using the mathematical concepts of sets, > > functions, and relations, he should use standard terminology, where > > "standard" means the same as in some mathematics book. It is like saying > > that if he wants to speak in English he should use words according to > > the meanings as given in an English dictionary. > > Certainly. In very much the same way as you think you can talk about > phenomena in the atomic domain by using the standard terminology from > Newtonian mechanics. While Quantum Mechanics instead uses a different > terminology that you seem not to be able to comprehend. It is truly amazing how much trouble you have reading. How in the world did you come to the erroneous conclusion that I was discussing Newtonian mechanics? I see now why you don't bother to read any math books. Books really aren't of much use if you have trouble reading. -- David Marcus
From: David Marcus on 24 Oct 2006 22:17 Sebastian Holzmann wrote: > mueckenh(a)rz.fh-augsburg.de <mueckenh(a)rz.fh-augsburg.de> wrote: > > > > Sebastian Holzmann schrieb: > >> Let's assume that ZFC - AoI is consistent, otherwise the statement is > >> void. Let \phi_n be a sentence in the language of set theory that > >> encodes the statement "There exists a set that has at least n elements" > >> (you can formulate this one as a homework problem). > > > > Perhaps you do another homework first: Why should such such a sentence > > be correct? It is not difficult to encode the sentence: Card(Q) > > > Card(R). Is that a proof? > > Such a sentence should not be "correct". Perhaps you should think of it > as a request for a certain property. Can you formulate it in the > language of set theory? Apparently, Muechenheim has only read the introduction of one set theory book and some of Cantor's papers. > It is a good exercise when you want to take part > in discussions about mathematical logic. > > Of course a sentence "Card(Q) > Card(R)" is not a proof. Please consult > a book on mathematical logic, set theory and model theory. -- David Marcus
From: David Marcus on 25 Oct 2006 00:28
Lester Zick wrote: > On Mon, 23 Oct 2006 22:24:16 -0400, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > >MoeBlee wrote: > >> mueckenh(a)rz.fh-augsburg.de wrote: > >> > If you claim that what you call modern set theory has a deviating > >> > definition of infinity, then I am not interested in your theory. > >> > >> This is not a matter of defining 'is infinite'. And if you're not > >> interested in Z set theory, then fine. But then you don't claim that > >> your argument about trees in Z set theory? I take it that your argument > >> about trees is in your informal understanding of pre-formal Cantorian > >> set theory. And I am not interested in your informal understanding of > >> pre-formal Cantorian set theory as if your informal understanding of > >> pre-formal Cantorian set theory has anything to do with formal > >> mathematics. > > > >That is rather remarkable. On the one hand, Mueckenheim claims standard > >set theory is inconsistent, but on the other he makes it clear that what > >he calls "set theory" is not standard set theory. Do you think he really > >thinks that standard set theory is inconsistent despite admitting that > >he hasn't read anything written on the subject since Cantor? > > Is there not an inconsistency regarding containment in standard set > analysis? Not that I (or any mathematicican) know of. I would think this fact would be obvious from the discussion on sci.math. -- David Marcus |