Cantor Confusion
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From: mueckenh on 8 Oct 2006 04:14 Tonico schrieb: > What taxpayers and where have to pay whom for this ""ambiguous > nonsense"" ([*****]and it of course is neither[*****], but go an convince the > barbarians...!)?? Don't you get more shocked by taxes gone for arms > expending, corrupt politicians and useless ministeries? The existence of one shocking fact is not a reason to accept another one. > Does it REALLY > bother you that some rather tiny part of the budget of any developed > country goes for universities On the contrary, I would starve without that tiny part. > and an even tinier part reaches the maths > deparments?? On the contrary. But a tiny part of this tiny part serves to convince unsuspicious young students of such pervers nonsense like I marked above [*****]. That is corrupting youth. > Have you noticed that the developed, strong, wealthy > countries ALWAYS have good math departments in universities? And what > is "omega transactions, anyway?!? I don't think that is a meaningdul > notion at all...who said it was, why, where and for what? For set theory. Any bijection between infinite sets contains omega elements. Whether you understand the vase experiment as a dynamic set of acts evolving in time or as a static set of facts simply existing is your choice. Set theory prefers the latter. > ******************************************************************** > > > > Good, that's how this is suposed to work: you can follow > > > your intuition in maths, but be sure to apply LOGIC, AXIOMS and reason > > > to confirm your intuition. > > > > Apply simply the knowledge that the contents of the vase grows, in > > infinity. No axiom is powerful enough to yield the contrary. This story > > only tells us that, if both sides of infinity are considered > > 1) Before noon every ball comes out of the vase > > 2) Before and at noon there are more balls in the vase than have come > > out > > then the axioms yield a contradiction. > > **************************************************************************** > What does the sentence "...the contents of the vase grows in infinity" > mean at all?? The contents does never decrease. > It sounds just like the christian fundie sentence "I love > you in Christ": what does this mean, in the holy name of Woody > Allen?!?!? And axioms can yeild whatever they want: that's what they're > axioms for! If a set of axioms yields the theorems A and nonA, then this set is useless. The axioms of ZFC yield the theorems "the vase is empty at noon" and "the vase is not empty at noon". >Now that they are consistent, sound axioms is another > matter for another discussion. They are just for discussing the vase-Gedankenexperiment. Otherwise Fraenkel and Levy would not have mentioned it (the Tristram Shandy version) in their book on set theory. > And what are "both sides" of infinity?? If you have not yet grasped it, then you seem incapable of learning it. > The left and right one, or what?! > What, in the name of insanity, are you talking about, dude?? Try at least to hide your bad education. Regards, WM
From: mueckenh on 8 Oct 2006 04:16 Tonico schrieb: > Not even Brouwer and his rather > weird intuitionist movement could, imfho., have used such nonsense to > defend their ideas... Oh, it seems I am in good company, in your eyes. Regards, WM
From: mueckenh on 8 Oct 2006 04:18 Virgil schrieb: > In article <1160223586.604282.269450(a)h48g2000cwc.googlegroups.com>, > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > > Tonico wrotef: > > > > > Maths, just like the other sciences, isn't grounded on dogma, and > > > people forwarding REASONABLE, well-based objections, opinions or ideas > > > on whatever are always welcome. > > > > _There_ is your problem! Ask Virgil, and the other mathematicians here: > > > > MATHEMATICS IS _NOT_ A SCIENCE > > > > And therefore there is NO guarantee that it "isn't grounded on dogma". > > > HdB's version of mathematics certainly seems to be grounded in dogma. > > My mathematics is merely grounded on determining what can be derived > from a given set of axioms. But you cannot derive that the vase is not empty at noon from the observation that its contents cannot decrease? Regards, WM
From: mueckenh on 8 Oct 2006 04:19 William Hughes schrieb: > Ok. Let's call a day a "numbered day", if we are able > to associate the day with a specific natural number. So day > 5,341,134,322, is a numbered day, but the present day is not > a numbered day. The question is now: "Can X write about > each numbered day?" The question is easy to answer, but this X is a poor example, because there are far better ones like Tristram shandy and the vase, yielding sharper contradictions. 1) Every ball will have left the vase at noon. 2) At noon there are more balls in the vase than at any time before. Regards, WM
From: mueckenh on 8 Oct 2006 04:28
Virgil schrieb: > > We know, not by > > intuition, but by logic, that the vase at any time contains more balls > > than have escaped. > > Absolutely false. Bold words, but unfortunately simply wrong. The contents of the vase increases any time by 9 balls. > Before any balls are put in the vase, it is empty, and > after al balls have been removed from the vase it is equally empty. > It is only between these time that there are any balls in the vase at > all. > We have a contradiction n ZFC 1) Every ball will have left the vase at noon. 2) At noon there are more balls in the vase than at any time before. > > > And of course, this is also valid too for noon, if > > omega transactions is a meaningful notion at all. > > > What in blazes are "omega transactions"? An ordered set of countably infinitely many elements. > > > To assert that at > > noon (finished infinity, actualized transfinity) the vase is empty is > > not counter-intuitive but it stupid. > > But nowhere near as stupid as claiming that balls that have been removed > are still there. You claim that all have been removed although you do not know anything about noon. > > 1) Before noon every ball comes out of the vase > > 2) Before and at noon there are more balls in the vase than have come > > out > > then the axioms yield a contradiction. > > "Mueckenh" presumes some sort of "continuity" at noon, but the whole > process is discontinuous at each time of change. If it is meaningful to talk about *all* elements of an infinite set, then it is meaningful to consider the result of all transactions. > > The function which counts balls in the vase as a function of time jumps > discontinuously when any ball is inserted and also when any ball is > removed. Since noon is a condensation point of such discontiuities, it > is bootless to insist that it be a point of psuedocontinuity such as > "Mueckenh" claims. Therefore it is also false to conclude from the bijection of natural numbers and outcoming balls that no ball remains in the vase. You apply just this pseudocontinuity. > "Mueckenh" is certainly hopeless. With respect to become an adherent of your religion, yes. Regards, WM |