An uncountable countable set
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From: Randy Poe on 5 Oct 2006 11:16 Tony Orlow wrote: > > That assumes that there would have to be a "last ball", which equally > > assumes that there would have to be a "last natural number", which > > destroys TO's analysis. > > Uh, no, the very conclusion that the vase empties, when at most one ball > is removed at a time, implies that there is a last ball removed, but > that's impossible as I've shown. Right up to a point. The statement that there is a ball which takes the vase from full to empty, a TRANSITION to empty, requires that there be a last ball. However, the statement that the vase is empty at time T merely requires that every ball put in before T is also removed before T. - Randy
From: Lester Zick on 5 Oct 2006 11:42 On 4 Oct 2006 16:11:00 -0700, cbrown(a)cbrownsystems.com wrote: >imaginatorium(a)despammed.com wrote: >> Tony Orlow wrote: [. . .] >I think this is exacly the problem that occurs with Tony, HdB, and many >others. (Ross, WM and Zick have other, uh, issues). Somehow I rather doubt truth is another, um, issue. ~v~~
From: mueckenh on 5 Oct 2006 12:39 Virgil schrieb: > If we alter the problem to start with all the balls in the vase and > remove them according to the original schedule then every ball spends at > least as much time in the vase as before, but not everyone will see that > the vase is empty at noon. This variant shows for another time that the result is completely undefined. (I assume you made a Freudian typo but wanted to say: "but now everyone will see that the vase is empty at noon". And you are right, at least for those who think that all numbers exist.) > > Those who argue that having the balls spend less time in the vase leaves > more of them in the vase as noon, have some explaining to do. No, for they know that to talk about all the balls yields nonsense. Here is another proof: Put 10 balls in A and remove two, one of which is put in B and the other one is put in C. Do you continue to believe that all the balls are in B at noon? The symmetry of the problem strongly indicates that C contains all balls at noon of 50 % of all experiments. Regards, WM
From: mueckenh on 5 Oct 2006 12:40 Virgil schrieb: > In article <1159799981.773875.190290(a)b28g2000cwb.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: > > > Han de Bruijn schrieb: > > > > > > > What does your "mathematics" say the answer to this > > > > question is, in the "limit" as n approaches infinity? > > > > > > My mathematics says that it is an ill-posed question. And it doesn't > > > give an answer to ill-posed questions. > > > > You are right, but the illness does not begin with the vase, it beginns > > already with the assumption that meaningful results could be obtained > > under the premise that infinie sets like |N did actually exist. > > That opinion is a minority opinion. Good taste has always been a matter of the minority (August Everding, the late director of the Bavarian theatres, translation by me). Regards, WM
From: mueckenh on 5 Oct 2006 12:43
Dik T. Winter schrieb: > > By the only meaningful and consistent definition: A n eps |N : > > |{1,2,3,...,2n}| = 2*|{2,4,6,...,2n}|. > > Do you challenge its truth? > > No, I never did. But you draw conclusions about it about the set N. Indeed, > for each finite n, it is true. But this is *not* a proper definition for > the amounts involved in infinite sets. Given two infinite sets A and B, > by what method do you determine whether A has more elements than B, or > the other way around? Are there more Gaussian integers than Eisenberg > integers, and if so why? And if not, why not? There are no complete infinite sets. Therefore it is useless to find out whether one of them is larger than another. |{1,2,3,...,2n}| = 2*|{2,4,6,...,2n}| is only valid for n eps |N, i.e., for finite sequences. > You attack the existence of an infinite sequence, and so also the existence > of an infinite set. So be it. But that is just a negation of the axiom of > infinity. With that axioms such things do exist. I would like to know whether numbers exist, not what axioms do say about them. Numbers 1 and 2 and 3 exist without any axioms. Number omega does not exist, with and without any axiom. Without axiom it is clear. With the axiom INF you see the results. You must insist on the silliest ideas (like covering up to every but not covering every). Regards, WM |