Cantor Confusion
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From: MoeBlee on 6 Dec 2006 14:40 mueckenh(a)rz.fh-augsburg.de wrote: > stephen(a)nomail.com schrieb: > > > If you think sets grow, then you do not understand set theory. > > I know that in modern set theory sets do not grow. It's good that you finally came around to that conclusion. > But I heavily doubt the relevance of modern set theory. It's relevant to me as an axiomatization of ordinary mathematics as well as of meta-mathematics and also interesting onto itself as an abstract study. MoeBlee
From: MoeBlee on 6 Dec 2006 14:46 Eckard Blumschein wrote: > On 12/5/2006 10:54 PM, Virgil wrote: > > EB should read what axioms of extensionality actually says before > > pontificating. > > Roughly speaking, it just claims that a set is unambiguously determined > by its elements. If i recall correctly A=B<-->(A in B and B in A) "A=B<-->(A in B and B in A)" That is just INCOMPETENT. You recall TERRIBLY incorrectly! MoeBlee
From: Virgil on 6 Dec 2006 15:22 In article <1165402679.785191.310490(a)80g2000cwy.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > > What limits thought to only the accessible part of the universe? > > The fact that any brain consists of not more than this limited part of > the universe. So because my brain exists in the USA, I cannot think about Europe?
From: Virgil on 6 Dec 2006 15:29 In article <1165402878.126278.296600(a)73g2000cwn.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > > > I think, nobody would oppose to dividing the edges merely in two halves > > > each. If the series 1 + 1/2 + 1/4 + ... yields 2, then we can extend > > > this knowledge to bijections too. > > > > In order to have a bijection from edges to paths one must have a rule > > which assigns each edge ,in its entirety, to some path. > > > > WM does not do this, ergo has no bijection. > > In order to see that a ball which is contained in a closed box cannot > escape, we need not have a rule determining its position. Quantum theory says the ball can escape, though with very low probability. > > So is the ratio between paths and edges. The number of paths is > irrevocably bounded by the number of edges. This is so for any finite > part of the tree. In order to reverse this ratio, there must be parts > of paths which do not consist of edges. Since WM is mapping sequences of branches to paths, rather than edges to paths, the most he can show is that the number of sequences of branches equals the number of paths. But that is a given. > > In fact there are not > less edges than paths. WM is befuddled by looking at finite trees.
From: Virgil on 6 Dec 2006 15:32
In article <1165403177.893469.76590(a)j72g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Dik T. Winter schrieb: > > > In my mind. I can reasonably think about the set of all natural numbers. > > Honest, I have no problem with it. > > You believe you could. That is a difference to "can". Other people > think they can reasonably think of having an immortal soul. While I do not think any such thing, I am not so arrogant as to suppose others incapable of thinking things that I am not able to think. WM's arrogance is oppressive. |