Cantor Confusion
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From: Bob Kolker on 30 Nov 2006 07:38 Eckard Blumschein wrote: > > Really? Fraenkel, 2nd ed. 1923, approved Cantor having managed not just > to battle but also refute an assertion by Gauss. > Is there any evidence for this proud claim? No. > Whenever Cantor declared mathematicians like Aristotele, Locke, Locke and Aristotle were NOT mathematicians. Aristotle was at most, a logician or an ethicist or a political "scientist" or a literarary critic. As a scientist he was a failure. Why? He didn't check. Bob Kolker
From: Bob Kolker on 30 Nov 2006 07:39 Eckard Blumschein wrote: > > > Large enough is certainly not qualitatively different enough, infinity > is the location where two parallel lines are thought to meet each other, > and division by zero has been forbidden because it yields anything. Division by zero in a field yeilds a contradiction. That is why it is forbidden. 1/0 = x (for some x in the field) implies 1 = 0*x = 0. That simply will not do. Bob Kolker
From: Eckard Blumschein on 30 Nov 2006 09:28 On 11/30/2006 3:19 AM, Dik T. Winter wrote: > In article <1164816790.379338.139370(a)h54g2000cwb.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: > > 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. > > There is nothing in that that shows that a set is not a fixed entity. > You are able to produce bigger and bigger sets, but they are all > different. So far I recall "the set IN of naturals is countable". I understood set theory means a hypothetical (alias fictitious) set off all natural numbers. Maybe, you are not aware of some shizophrenia in Cantor's concept. He actually imagines infinity like a quantity, like someting "festes" (concrete). At the same time he proofs by bijection, that the naturals are contable. The naturals are of course countable if considered one by one. However the entity of all naturals only exists like an uncountable fiction.
From: MoeBlee on 30 Nov 2006 13:12 mueckenh(a)rz.fh-augsburg.de wrote: > MoeBlee schrieb: > > > 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. > > Your "proof" concerns less than 10^100 elements. You are not even able > to express some natural numbers of this domain, but you insist that > there was a proof concerning all of them. A ridiculous > self-overestimation. You must be running a very high fever. In the proof I've mentioned, there's no mention nor dependency on any claims limited to 10^100 elements. MoeBlee
From: MoeBlee on 30 Nov 2006 13:23
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. 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. > > not that any given set itself grows, let alone that there are > > finite sets without a largest element (!). > > You misunderstand Fraenkel and you misunderstand me. Small wonder. I > did not say that Frankel talks about these growing sets with the same > meaning as I do. Please read carefully (try it for one time). I wrote: > " We have to accept that there are sets which are capable of growing, > *as Fraenkel et al. express it*. Nope I understand and represented accurately. Your notion of what Fraenkel, Bar-Hillel, and Levy say is terribly incorrect and the inferences you draw are ludicrous. MoeBlee |