An uncountable countable set
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From: David R Tribble on 2 Oct 2006 16:20 Tony Orlow schrieb: >> Do I "misunderstand" that if you remove balls 1, then 11, then >> 21, etc, that the vase will NOT be empty? > mueckenh wrote: >> 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. > Tony Orlow wrote: > 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. How do you know the membership status of each element if you have no way to distinguish the elements from each other?
From: David R Tribble on 2 Oct 2006 16:27 Tony Orlow wrote: >> You drew that from my suggestion of the number circle, and that ...11111 >> could be considered equal to -1. Since then, I looked it up. I'm not the >> first to think that. It's one of two perspectives on the number line. >> It's either really straight, or circular with infinite radius, making it >> infinitesimally straight. The latter describes the finite universe, and >> the former, the limit. But, you knew that, and are just trying to have fun. > David R Tribble wrote: >> You are drawing geometric conclusions that are not warranted. >> The Projective Real Line is simply R U {oo}. Adding unsigned oo >> to the set allows certain arithmetic operations to be performed >> that are undefined in the regular real set. >> >> But simply adding the limit point oo to the set does not actually make >> it a "circle", because oo has no predecessor or successor, and >> certain operations like oo+1 and oo+oo are still meaningless within >> the set. > Tony Orlow wrote: > You do realize that my statements involve a considerable amount of > personal reflection, don't you? There is more to the number circle than > "proven". In the binary number circle, "100...000" is both positive and > negative infinity. By what axioms? David R Tribble wrote: >> See: >> http://en.wikipedia.org/wiki/Projective_line#Real_projective_line >> http://en.wikipedia.org/wiki/Division_by_zero#Real_projective_line >> http://en.wikipedia.org/wiki/Extended_real_number_line >> >> You obviously have something else in mind when you talk about >> the "number circle". Perhaps you could actually define it some time? > Tony Orlow wrote: > There are a number of concepts in this area. Get acquainted with those > pages, think, and come back and talk. And that will allow you to define the terms of your number theory? You underestimate the degree to which we understand your theories. It's pretty obvious that the mathematically inclined among us follow what you're saying, because, honestly, it's really not that complicated or profound. Most of it also happens to be self-contradictory, which is where most of us have a problem "seeing" it. Which makes it incumbent upon you to define your ideas a little more clearly and a lot more formally. It's not a failing on my part that your ideas are not consistent, but rather a failing on your part not to recognize the logical conclusions that prove these inconsistencies.
From: Randy Poe on 2 Oct 2006 17:14 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. Why is it ill-posed? Is it ill-posed for n=101? > > you have a set of n balls labelled 0...n-1. 0 to 100, for example. > > ball #m is added to the vase at time 1/2^(m/10) minutes > > before noon. So ball 100 is added 1/2^10 minutes before noon. All the other balls are added before that. > > ball #m is removed from the vase at time 1/2^m minutes > > before noon. Ball 100 is removed at 1/2^100 minutes before noon. All the other balls are removed before that. > > how many balls are in the vase at noon? Can you tell me why that's ill-posed? - Randy
From: Lester Zick on 2 Oct 2006 18:18 On Mon, 2 Oct 2006 16:43:15 +0000 (UTC), stephen(a)nomail.com wrote: >Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >> stephen(a)nomail.com wrote: [. . .] >So one wonders what criteria you used to determine that >this infinity cannot be approached via limits. Which kinda takes us back to the definition of infinity wouldn't you say? If infinity can be approached via limits infinity would have to refer to the number of infinitesimals and if not infinity couldn't be approached via limits. ~v~~
From: Virgil on 2 Oct 2006 18:31
In article <452160ef(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Randy Poe wrote: > > 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? It is at a particular state at any particular time, but as the states do not form a continuum, one gets jump discontinuities in the number of balls in the vase in a neighborhood of each relevant time. And in every neighborhood of noon, there are infinitely many such discontinuities. |