An uncountable countable set
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From: Virgil on 5 Oct 2006 14:44 In article <1160036576.204353.290740(a)i3g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Tony Orlow schrieb: > > > 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. > > There are two equivalent truths: > > (1) (Each) ball number n will come out before noon. > (2) When ball number n comes out, more than n balls remain in the vase. > > Both are absolutely correct. This shows that one can not consistently > calculate with infinity. While this prohibits the vase from becoming empty before noon, it does not prevent it from being empty at noon. The "number of balls in the vase", f(t), as a function of time, t, has an essential discontinuity at t = noon. Lim_{t -> noon-} f(t) = oo Lim_{t -> noon+} f(t) = f(noon) = 0
From: Virgil on 5 Oct 2006 14:46 In article <9b534$4524cc4b$82a1e228$17930(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Mike Kelly wrote: > > > Han de Bruijn wrote: > > > >>Quote [ Randy Poe ] : Physicists also > >> > >>>realize that things can exist in mathematics that aren't even > >>>approximations of a physical realizable. That aren't physically > >>>sensible in other words. > >> > >>That's only true for non-disciplinary mathematics. > > > > What is non-disciplinary mathematics? Is it not mathematics? > > It is mathematics without the discipline. > > Han de Bruijn It is mathematics without HdB's discipline, but it has sufficient discipline of its own to get by with. HdB's idea of "discipline" is too much lake Sadism to suit most mathematicians.
From: Virgil on 5 Oct 2006 14:49 In article <9b534$4524cc4b$82a1e228$17930(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Mike Kelly wrote: > > > Han de Bruijn wrote: > > > >>Quote [ Randy Poe ] : Physicists also > >> > >>>realize that things can exist in mathematics that aren't even > >>>approximations of a physical realizable. That aren't physically > >>>sensible in other words. > >> > >>That's only true for non-disciplinary mathematics. > > > > What is non-disciplinary mathematics? Is it not mathematics? > > It is mathematics without the discipline. > > Han de Bruijn It is mathematics without HdB's sadistic version of discipline.
From: Virgil on 5 Oct 2006 14:53 In article <1160041475.161854.286530(a)m7g2000cwm.googlegroups.com>, Han.deBruijn(a)DTO.TUDelft.NL wrote: > Mike Kelly schreef: > > > > > I have looked in several calculus books, starting with Apostol's, and > > > > found no such thing in any of them. They are all careful to say that, > > > > absent convergence, limit definitions say nothing about what happens. > > > > > > There are no other definitions of the infinite than limit definitions. > > > > There obviously *are* other definitions, you just do not approve of > > them. Why should anyone particularly care for your likes and dislikes? > > Precisely! Why should anyone particularly care for your A(n,0) = 0 ? Because at t = 0 each and every ball has been removed, despite HdB's attempts to block those removals. > > Han de Bruijn
From: Virgil on 5 Oct 2006 14:59
In article <1160043857.204324.235890(a)m73g2000cwd.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > > > By the way, please switch to the thread "Cantor > > > Confusion" because this one has become too lengthy and, at home, I have > > > only a slow internet access. So I am not able to follow this thread > > > firmly. > > > > Oh. I did not know that slow internet access made long threads more > > difficult to follow than short threads. > > It lasts a long while until all is loaded again, after I have posted. > This problem, however, exists only during the weekends. But this thread > is too long. I am not able and willing to read all contributions. > > > I see no reason to shift the > > subject. And certainly not to a subject for which a thread already does > > exist. > > The original subject of this thread is no longer under discussion here. > > > Regards, WM Get a more efficient NG reader, then. Google sucks for most NG tasks. There are a variety of them available for free which do not load an entire thread, but only current postings. I use MT-Newswatcher on a Mac, and it is great. |