An uncountable countable set
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From: Virgil on 2 Oct 2006 15:22 In article <4521035d(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > Belonging to a particular set distinguishes its members from all the > > non-members, so the truth of "x is a member of set A" depends on which x > > and which A one is considering. > > So, that would be a "no". Of course, a set can also be associated with a > property which holds true for all members of the and not for > non-members, but you wouldn't want to go there. Been there. Done that. Got the Tee shirt, but long since wore it out.
From: Virgil on 2 Oct 2006 15:26 In article <4521128b(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > They are saying that the vase empties because every ball inserted is > removed. They agree that this does not occur before noon, when there are > always balls in the vase, but by noon the vase is empty. But they cannot > say that, even though there are balls before noon, and none at noon, > that the vase "became empty" at noon, because they are claiming "the > limit doesn't exist". So, don't ask me what they mean. I can't figure it > out. The lack of any "limit" and the emptyiness at noon are only two of many quite straightforward things that TO cannot figure out.
From: Virgil on 2 Oct 2006 15:32 In article <1159797618.679513.221400(a)i3g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil 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? > > > > I challenge the "truth" of its being the ONLY meaningful and consistent > > definition. > > > If we insist on unique results in mathematics, then this definition and > the bijection exclude each other. Uniqueness of results depends on what one is doing. If one is considering finding a possible order relation on a set of two or more elements, would "Mueckenh" insist that there is a unique result? Does "Mueckenh" claim that there is only one function mapping {1,2,3,...} to {2,4,6,...} or vice versa?
From: Virgil on 2 Oct 2006 15:36 In article <1159798407.217254.275710(a)m7g2000cwm.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Tony Orlow schrieb: > > > > > This is an extremely good example that shows that set theory is at > > > least for physics and, more generally, for any science, completely > > > meaningless. Because the numbers on the balls cannot play any role > > > except for set-theory-believers. > > > > Yes. I was flabbergasted by this example of "logic". The amazing thing > > is, set theory is supposed to apply where we know nothing except for the > > membership status of each element in a set, and yet, here is applied > > this property of labels that set theorists claim is crucial to answering > > the question. Set theory in the finite sense is a fine thing, but when > > it comes to the infinite case, set theorists don't even know anymore > > what they're TRYING to do. > > One should think that set theory, if useful at all, should be capable > of treating problems like this. But here we see it fail with > gracefulness and mastery. > > Set theorists always see only the one ball escaping the vase but not > the 9 remaining there. So they can accept that there are as many > natural numbers as rational numbers. I cannot understand how this > theory could invade mathematics and how I could believe it over many > years without a shade of doubt. > > Regards, WM 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. 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.
From: Virgil on 2 Oct 2006 15:38
In article <d0348$45211ed2$82a1e228$21748(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Tony Orlow wrote: > > > They are saying that the vase empties because every ball inserted is > > removed. They agree that this does not occur before noon, when there are > > always balls in the vase, but by noon the vase is empty. But they cannot > > say that, even though there are balls before noon, and none at noon, > > that the vase "became empty" at noon, because they are claiming "the > > limit doesn't exist". So, don't ask me what they mean. I can't figure it > > out. > > So far for Tony Orlow. But neither can Han de Bruijn, neither can David > Petry, neither can Wolfgang Mueckenheim, neither can Jeroen Boschma and > neither can 'snapdragon', neither can 'rennie nelson' - to mention only > a few others - nobody of them can figure out what they mean. Therefore > I wonder if this mainstream mathematics "solution" still has a majority > of yes-voters behind it. > > Han de Bruijn Of those who will bother to vote, yes. |