Cantor Confusion
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From: David Marcus on 7 Dec 2006 01:23 mueckenh(a)rz.fh-augsburg.de wrote: > MoeBlee schrieb: > > mueckenh(a)rz.fh-augsburg.de wrote: > > > No. We have to accept that there are sets which are capable of > > > growing, as Fraenkel et al. express it. Then we have finite sets without > > > a largest element. Then we describe reality correctly. > > > > You're a dishonest fool. > > If you continue to loose your self control in this way, then I will > have to cease discussing with you. If only you would do so. -- David Marcus
From: David Marcus on 7 Dec 2006 01:28 MoeBlee wrote: > mueckenh(a)rz.fh-augsburg.de wrote: > > MoeBlee schrieb: > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > No. We have to accept that there are sets which are capable of > > > > growing, as Fraenkel et al. express it. Then we have finite sets without > > > > a largest element. Then we describe reality correctly. > > > > > > You're a dishonest fool. > > > > If you continue to loose your self control in this way, then I will > > have to cease discussing with you. > > No loss of self-control. I comment as I see fit; and the most salient > thing about your latest postings is that they reveal you to be a > dishonest fool. Your choice to continue or cease posting in response to > my posts is yours alone. > > > > 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, > > > > That is nonsense. I know that you cannot recognize it. Only for the > > lurkers: If *different* sets generated by different axiom systems were > > meant, then Fraenkel et al. would not only have to talk about "growing" > > but also about "shrinking" or simply about differing sets. But they > > don't. > > One just needs to read and understand the section they wrote. On the > other hand, if what one does, as you do, is cruise the book looking for > out of context quotes to misconstrue and misrepresent, then > understanding is not required. It is an interesting way to read a book: Assume you already know what the book is saying, and look for quotes that can be stretched so as to vaguely support what you already believe. Then tell people that although the subject of the book (set theory) is nonsense, you've found a statement in the book that supports your incoherent claims. I suppose for some it takes less effort than the normal way of reading books. -- David Marcus
From: David Marcus on 7 Dec 2006 01:36 mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > > > It cannot have a cardinal number at all. We have no cardinals in > > > potential infinity. Cantor knew that. > > > > Piffle. > > > > Extending the concept of bijection from sets to potentially > > infinite sets is trivial. > > May be if you apply your personal definition of potentially infinity, > but not if you apply the generally accepted definition. Wow! A term, "potential infinity", that appears in no modern books or journals has a "generally accepted" definition! It must be generally accepted in the Antiquarian Bookshop. Care to state this generally accepted defintion in English? -- David Marcus
From: David Marcus on 7 Dec 2006 01:51 William Hughes wrote: > mueckenh(a)rz.fh-augsburg.de wrote: > > Please clarify a point of nomenclature. > Do you consider a potentially infinite > set contianing only finite elements > (e.g. the natural numbers) to be: > > 1. a set ? > 2. a finite set? May I trouble you to restate the definition of "potentially infinite set" that you are using? -- David Marcus
From: David Marcus on 7 Dec 2006 01:54
Eckard Blumschein wrote: > On 12/1/2006 3:03 PM, mueckenh(a)rz.fh-augsburg.de wrote: > > > If you use the term "set" (like for instance for your set A) as defined > > in set theory, then all the elements are "there" (where ever that may > > be). Therefore you cannot describe potential infinity by means of ZF or > > NBG set theory, unless you use completely different definitions of > > "set" etc. > > The trick with these axioms is: They do not really define the notion > set. Why not? Although, the word "characterize" would be better than "define". > Notice: Cantor's untennable definition Which definition are you referring to? > has not been substituted by a new and correct one but the oracle-like axioms. -- David Marcus |