An uncountable countable set
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From: Han de Bruijn on 5 Oct 2006 03:22 Virgil wrote: > In article <47d15$45236440$82a1e228$12308(a)news2.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>stephen(a)nomail.com wrote: >> >>>Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >>> >>>>We can say that the number of balls Bk at step k = 1,2,3,4, ... is: >>>>Bk = 9 + 9.ln(-1/tk)/ln(2) where tk = - 1/2^(k-1) for all k in N . >>>>And that's ALL we can say. The version of the problem used here is >>>>the first experiment in: >>> >>>>http://groups.google.nl/group/sci.math/msg/d2573fcb63cbf1f0?hl=en& >>> >>>Why can't we say that every ball that is added is also >>>removed? >>> >>> ball #m is added to the vase at time 1/2^(floor(m/10)) minutes >>> before noon. >>> >>> ball #m is removed from the vase at time 1/2^m minutes >>> >>>Every ball is removed before noon, no matter how many >>>balls there are. >> >>The question is: how many balls are there in the vase at noon. >>This question is meaningless, because noon is never reached. > > It was yesterday. At least here. Yes. Because there wasn't a Balls in a Vase problem at your place. Han de Bruijn
From: Han de Bruijn on 5 Oct 2006 03:27 Virgil wrote: > In article <b8b9$45236b93$82a1e228$13353(a)news2.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>Virgil wrote: >> >>>That the "series" diverges means that there is no such thing as a limit, >>>so that method does not say anything about the result. >> >>That method says there is no result at noon. > > Not so. That method merely says that IT cannot tell what happens at noon. Don't know who IT is. > It definitely does NOT say that there is no other method that can tell > what happens at noon. There is no other method. >>You can find this in any >>first year calculus text book. > > 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. Han de Bruijn
From: Virgil on 5 Oct 2006 03:30 In article <6829$4524b248$82a1e228$27138(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Randy Poe wrote: > > > Math has to be logical. It doesn't have to be physically > > realizable. > > Wrong. Math has to be an idealization which can be materialized again > into something that is physically realizable. Quote: Physicists also It is HdB who is wrong. HdB may be so limited that he cannot imagine anything not "physically realizable", but there is a lot of math that is not. > > > 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. The non-disciplinary mathematicians being the ones that do not go in for those masochistic games.
From: Han de Bruijn on 5 Oct 2006 03:31 Virgil wrote: > In article <161ca$4523bb80$82a1e228$8996(a)news2.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>imaginatorium(a)despammed.com wrote: >> >>>Han de Bruijn wrote: >>> >>>>The question is: how many balls are there in the vase at noon. >>>>This question is meaningless, because noon is never reached. >>> >>>Really? When's lunch, then? >> >>Time is _suggested_, but not present, in the Balls in a Vase problem. > > Without any time to put balls into the vase, the vase is empty. In real time there are no singularities. With the Balls in a Vase there is a singularity at noon. Therefore the quantity called "time" resembles real time sometimes, but not always. Han de Bruijn
From: Virgil on 5 Oct 2006 03:32
In article <c4b5a$4524b2bf$82a1e228$27138(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <47d15$45236440$82a1e228$12308(a)news2.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > >>stephen(a)nomail.com wrote: > >> > >>>Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > >>> > >>>>We can say that the number of balls Bk at step k = 1,2,3,4, ... is: > >>>>Bk = 9 + 9.ln(-1/tk)/ln(2) where tk = - 1/2^(k-1) for all k in N . > >>>>And that's ALL we can say. The version of the problem used here is > >>>>the first experiment in: > >>> > >>>>http://groups.google.nl/group/sci.math/msg/d2573fcb63cbf1f0?hl=en& > >>> > >>>Why can't we say that every ball that is added is also > >>>removed? > >>> > >>> ball #m is added to the vase at time 1/2^(floor(m/10)) minutes > >>> before noon. > >>> > >>> ball #m is removed from the vase at time 1/2^m minutes > >>> > >>>Every ball is removed before noon, no matter how many > >>>balls there are. > >> > >>The question is: how many balls are there in the vase at noon. > >>This question is meaningless, because noon is never reached. > > > > It was yesterday. At least here. > > Yes. Because there wasn't a Balls in a Vase problem at your place. On the contrary, there was one with all those balls pouring in and out of the vase, but at noon the vase was empty and shortly thereafter the vase itself vanished. |