Cantor Confusion
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From: Eckard Blumschein on 29 Nov 2006 12:15 On 11/29/2006 5:24 PM, mueckenh(a)rz.fh-augsburg.de wrote: We have to accept thart there are sets which are capable of > growing, as Fraenkel et al. expess it. While there are several books by Fraenkel: Einleitung in die Mengenlehre 2nd ed. 1923, 3rd ed. 1946, Gesammelte Abhandlungen Cantor, Dedekind 1932 Das Leben Georg Cantors 1932 Abstract set theory 1961 Lebenskreise - Aus den Erinnerungen eines j�dischen Mathematikers 1967 perhaps there is only one book by Fraenkel et al.: Foundations of Set Theory 1958. Correct? > Then we have finite sets without > a largest element. Why not with a growing largest element? Regards, Eckard
From: MoeBlee on 29 Nov 2006 13:12 mueckenh(a)rz.fh-augsburg.de wrote: > MoeBlee schrieb: > > > > > I think if one swells to explosion about his knowledge of set theory, > > > he should at least know the very foundation. But I know, that you do > > > not even understand the simple texts of Fraenkel et al. > > > > No, YOU radically MISunderstand what Fraenkel, Bar-Hillel, and Levy > > wrote. > > How can you judge about that without the slightest idea of what they > wrote? Quite a while ago I had read that whole book. Upon your mentioning the quote, I re-read the quote in the book, re-read the section in which the quote appears, and re-read the chapter in which the section appears, and re-read several other parts of the book. > Only for the lurkers: Fraenkel et al. write: "Platonistic point > of view is to look at the universe of all sets not as a fixed entity > but as an entity capable of "growing", i.e., we are able to "produce" > bigger and bigger sets." That's part of what they wrote. You need to UNDERSTAND the section and the discussion leading to that quote to understand it. You don't. > So a set (like the set of all sets) is not a > fixed entity. WRONG. You just keep saying that, but ignore the rest of Fraenkel, Bar-Hillel, and Levy's discussion, and also you just keep skipping past my own on-point replies to you on this matter. > >Meanwhile, you are ignorant of even such basic set theory as > > proving the existence of an identity function. > > I think of a correct proof, not of blowing hot air. If you can't think of a proof that the identity function exists for any set, then you are ignorant of basic set theory. > > The information I require about the very basis of this discussion was > > specified in my previous posts - the ones I wrote a couple of week ago > > and which I mentioned yet again, but which you yet again ignore. I took > > the effort to compose those questions for you at that time. If you want > > me to consider your argument, then please respond to those posts. I'm > > not inclined to recompose my questions for you again after I already > > carefully composed them. > > Which posts? When posted? The ones Lester Zick responded to with his "my way or the highway" remark. > By copy and paste you should be able to > repeat those questions. I already took the time to compose the posts. I'm not inclined to use up more of my time tracking them down for you after you've ignored them. Find them on your own time, or don't, but then don't expect me to address your tree argument until you do answer them. > I saw only the question whether I believed that > a proof in ZFC was possible. Then you didn't read the posts. > Should this question decide whether such a > proof is really possible? Of course not. What a silly question. MoeBlee
From: MoeBlee on 29 Nov 2006 13:17 mueckenh(a)rz.fh-augsburg.de wrote: > > The reason I believe it's a theorem of Z set theory that there is a > > bijection between the set of natural numbers and the set of ordered > > pairs of natural numbers is because I've studied at least one proof. > > It is believed to be a proof. But it isn't a proof. It is demonstarted > for few symbols. I don't know what you mean by 'demonstrated for few symbols'. Meanwhile, there does exist a proof in Z set theory that there exists a bijection between the set of natural numbers and the set of ordered pairs of natural numbers. MoeBlee
From: Virgil on 29 Nov 2006 13:26 In article <1164816790.379338.139370(a)h54g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > MoeBlee schrieb: > > > > > I think if one swells to explosion about his knowledge of set theory, > > > he should at least know the very foundation. But I know, that you do > > > not even understand the simple texts of Fraenkel et al. > > > > No, YOU radically MISunderstand what Fraenkel, Bar-Hillel, and Levy > > wrote. > > How can you judge about that without the slightest idea of what they > wrote? Only for the lurkers: Fraenkel et al. write: "Platonistic point > of view is to look at the universe of all sets not as a fixed entity > but as an entity capable of "growing", i.e., we are able to "produce" > bigger and bigger sets." So a set (like the set of all sets) is not a > fixed entity. In ZF, ZFC and NBG there is no such thing as a set of all sets. And note thet the F in ZF is for Fraenkel. > > >Meanwhile, you are ignorant of even such basic set theory as > > proving the existence of an identity function. > > I think of a correct proof, not of blowing hot air. Then how is it that you continually blow hot air but have never provided a correct proof of anything? And few if any incorrect ones!
From: MoeBlee on 29 Nov 2006 13:26
mueckenh(a)rz.fh-augsburg.de wrote: > No. We have to accept thart there are sets which are capable of > growing, as Fraenkel et al. expess it. Then we have finite sets without > a largest element. Then we describe reality correctly. You're a dishonest fool. I've already explained to you, as you should have read for yourself in the original source, that what Fraenkel, Bar-Hillel, and Levy mean by the universe of sets "growing" (THEIR scare quotes) is that different axioms yield different universes of sets, not that any given set itself grows, let alone that there are finite sets without a largest element (!). MoeBlee |