An uncountable countable set
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From: David R Tribble on 2 Oct 2006 14:40 Virgil wrote: >> Except for the first 10 balls, each insertion follow a removal and with >> no exceptions each removal follows an insertion. > Tony Orlow wrote: > Which is why you have to have -9 balls at some point, so you can add 10, > remove 1, and have an empty vase. "At some point". Is that at the last moment before noon, when the last 10 balls are added to the vase?
From: Tony Orlow on 2 Oct 2006 14:40 Han de Bruijn wrote: > stephen(a)nomail.com wrote: > >> Han.deBruijn(a)dto.tudelft.nl wrote: >> >>> Worse. I have fundamentally changed the mathematics. Such that it shall >>> no longer claim to have the "right" answer to an ill posed question. >> >> Changed the mathematics? What does that mean? >> The mathematics used in the balls and vase problem >> is trivial. Each ball is put into the vase at a specific >> time before noon, and each ball is removed from the vase at >> a specific time before noon. Pick any arbitrary ball, >> and we know exactly when it was added, and exactly when it >> was removed, and every ball is removed. >> Consider this rephrasing of the question: >> >> you have a set of n balls labelled 0...n-1. >> >> ball #m is added to the vase at time 1/2^(m/10) minutes >> before noon. >> >> ball #m is removed from the vase at time 1/2^m minutes >> before noon. >> >> how many balls are in the vase at noon? >> >> 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. > > Han de Bruijn > Actually, that question is not ill-posed, and has a clear answer. The vase will be empty, if there is any limit on the number of balls, and balls can be removed before more balls are added, but it is not the original problem, which states clearly that ten balls are inserted, before each one that is removed. That's the salient property of the gedanken. Any other scheme, such as labeling the balls and applying transfinitology, violates this basic sequential property, and so is a ruse. Tony
From: Tony Orlow on 2 Oct 2006 14:43 mueckenh(a)rz.fh-augsburg.de wrote: > Han de Bruijn schrieb: > >> stephen(a)nomail.com wrote: >> >>> Han.deBruijn(a)dto.tudelft.nl wrote: >>> >>>> Worse. I have fundamentally changed the mathematics. Such that it shall >>>> no longer claim to have the "right" answer to an ill posed question. >>> Changed the mathematics? What does that mean? >>> >>> The mathematics used in the balls and vase problem >>> is trivial. Each ball is put into the vase at a specific >>> time before noon, and each ball is removed from the vase at >>> a specific time before noon. Pick any arbitrary ball, >>> and we know exactly when it was added, and exactly when it >>> was removed, and every ball is removed. >>> >>> Consider this rephrasing of the question: >>> >>> you have a set of n balls labelled 0...n-1. >>> >>> ball #m is added to the vase at time 1/2^(m/10) minutes >>> before noon. >>> >>> ball #m is removed from the vase at time 1/2^m minutes >>> before noon. >>> >>> how many balls are in the vase at noon? >>> >>> 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. > > Regards, WM > It exists, it's just not well "defined". Yes it has a definition, but it has no discernible boundary. On the finite scale it's "way out there", ad on the infinite scale, it's basically the same as the origin. Omega is a phantom not worth concentrating on. Please see my other comment on this question. :) Tony
From: Tony Orlow on 2 Oct 2006 14:55 Ross A. Finlayson wrote: Hi Ross - Nice to see you. I hope you don't mind my adopting the Finlayson Numbers in my IFR sort of way. Cheers. > Tony Orlow wrote: >> Virgil wrote: >>> In article <45201554(a)news2.lightlink.com>, >>> Tony Orlow <tony(a)lightlink.com> wrote: >>> >>>> Virgil wrote: >>>>> A set is a container, and is not one of the objects that it contains. >>>> It is nothing more or less than its contents. >>> It is determined uniquely and entirely by its contents, as stated in the >>> axiom of extentionality. >> So we agree. There is nothing besides the members. > > Also, the members are only sets. Each member is a set? Well, yes, a set of property values which distinguish the members. > > I feel that I have been fair presenting construction of reason that > enable a rational person to make their own decision that, for example, > forceing uses a universal ordinal, I don't know much about "forcing", but it sounds kind of aggressive and not very nice. ;) the generic extension of N contains > no elements not in N yet bijects to R, Sequential form can be applied, I think, to any structure, if "forced". (Is that what that means?) the Borel/Combinatorics impasse, > and those as basically non-controversial. The impasse being over...what? Thanks in advance. :) > > I see some truths in some of the posters with alternative opinions, > also, I'm quite familiar with the standard viewpoint. I use my > viewpoint, which I develop in part myself. How dare you even feign that right? The nerve! > > These "infinities", as they are, are on the one hand various, as > infinite more various than any finite set could ever be, on the other > hand they each share certain properties and it seems at root they are > each irregular. Not just regular old numbers? Well I suppose not... > > Then, where some "least" infinite set has a given construction, there > are what are to most implicit aspects of that construction, implicit in > the sense of being true and not just unstated but known, to somebody, > thus true thus implicit. Like the set of multiples of neN, as n->oo? That would be one definition of the least, beyond the simplest. > > There is no universe in ZF where there are only sets, and not all of > them. There is no set of all sets, nor set of all ordinal (nor > cardinal) numbers as sets, no collection of a variety of other things > that are necessary for the establishment of certain formal arguments, > in ZF. There are objects, properties, and relations. Is there else? > > If you talk about and use those things, as most do with for universal > quantification over sets, then thus necessarily ZF is not sufficient > and is at once contradictory. With self, or reason? > > Oh, I'm not a crank. I am. :) Does that mean I'm wrong? Define "crank". I think it means someone who makes the entrenched "cranky". I think Goedel tells you the null axiom theory is > the only possible theory, where if it's inconsistent or incomplete it's > not A theory. > > Ross > According to most, that would mean, in the "light" of Godel, that "there is no theory". Is there a spoon? Have nice continuum, Tony
From: Tony Orlow on 2 Oct 2006 14:56
Randy Poe wrote: > Han.deBruijn(a)DTO.TUDelft.NL wrote: >> Randy Poe wrote: >> >>> Tony Orlow wrote: >>>> Randy Poe wrote: >>>>> Tony Orlow wrote: >>>>>> Han de Bruijn wrote: >>>>>>> Virgil wrote: >>>>>>> >>>>>>>> In article <d12a9$451b74ad$82a1e228$6053(a)news1.tudelft.nl>, >>>>>>>> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >>>>>>>> >>>>>>>>> Randy Poe wrote, about the Balls in a Vase problem: >>>>>>>>> >>>>>>>>>> It definitely empties, since every ball you put in is >>>>>>>>>> later taken out. >>>>>>>>> And _that_ individual calls himself a physicist? >>>>>>>> Does Han claim that there is any ball put in that is not taken out? >>>>>>> Nonsense question. Noon doesn't exist in this problem. >>>>>>> >>>>>> That's the question I am trying to pin down. If noon exists, that's when >>>>>> the vase supposedly empties, >>>>> Why does the existence of noon imply there is a time >>>>> which is the last time before noon? >>>>> >>>>> It doesn't. >>>> I never said it did. When did I say that? >>> I was responding to Han, who said that "If noon exists, that's when >>> the vase empties". >> HdB never said such a thing. > > You're right. So it's back to Tony. The quote is yours (Tony), so > just follow the attributes back to "if noon exists, that's > when the vase empties", and that's when you (Tony) > said such a thing. > > - Randy > Okay Randy, but does it, or not? Is it non-empty, then empty? Does this change in state occur before noon? After noon? Or, at noon? |