An uncountable countable set
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From: Han de Bruijn on 13 Oct 2006 03:32 Virgil wrote: > In article <1160669820.603144.288450(a)e3g2000cwe.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: > >>Dik T. Winter schrieb: >> >>> > > You question whether "all x in N" does exist, apparently. Based on >>> > > what? >>> > >>> > Based on the impossibility to index the positions of our 0.111..., >>> >>>False. >>> >>> > based on the vase, based on many other contradictions arising from "all >>> > x in N do exist". >>> >>>False. >>> >>>No proof given. >> >>No proof possible because every proof must be dismissed unless the game >>of set theory should perish. > > The "game of set" theory, as defined by ZF or NBG or something similar, > will survive "Mueckenh". We will see. The future is not what happens to us, but what we make of it. Han de Bruijn
From: Han de Bruijn on 13 Oct 2006 03:39 Randy Poe wrote about the Balls in a Vase problem: > Tony Orlow wrote: >>Specifically, that for every ball removed, 10 are inserted. > > All of which are eventually removed. Every single one. All of which are eventually inserted. Every single one. Thus the end result is _undefined_. Han de Bruijn
From: Han de Bruijn on 13 Oct 2006 03:42 Alan Morgan wrote: > In article <452e8c2a(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: >>What is sum(n=1->oo: 9)? > > I think you actually mean, what is 10-1+10-1+10-1.... > > It was recognized long before Cantor that there isn't a simple answer to > that question. It was recognized long before Cantor that there isn't an answer at all to a meaningless question. Han de Bruijn
From: Virgil on 13 Oct 2006 03:42 In article <14f3a$452f38d0$82a1e228$28478(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Randy Poe wrote about the Balls in a Vase problem: > > > Specifically, that for each particular ball (whatever you > > want to label it), there is a time when it comes out. > > Yes. And, at the same time, 10 others come in. So what? > > Han de Bruijn So which balls do not come out before noon? This is the same paradox as Hilbert's Hotel, which can be full and still have room for countably many more.
From: Virgil on 13 Oct 2006 03:44
In article <995cb$452f39c0$82a1e228$28834(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Mike Kelly wrote about the Balls in a Vase problem: > > > Ah, but noon is not a part of the sequence of iterations. No more than > > 0 is an element of the sequence 1, 1/2, 1/4, 1/8, .... > > Thus the question is whether the sequence (number of balls) converges. The number of balls seqeunce does not converge, but that does not prevent every ball being removed before noon. > > > The question asks how many balls are in the vase at noon. Not at some > > iteration. > > Well, it does not converge. So this question of yours is meaningless. According to the rules of the game, every ball is removed before noon, so the question of how many are left at noon is quite meaningful. |