Cantor Confusion
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From: Han de Bruijn on 4 Oct 2006 07:43 Tonico wrote: > Han de Bruijn ha escrito: > >>Wishful thinking on the part of William Hughes. A simple Google search >>will reveal that the army of 'sci.math' dissidents is steadily growing. > > ************************************************** > Zaas! Dissidents...from sci.math???? Didn't know somebody already > formed a political or social or economical or > whatever-that-isn't-science group called sci.math, and that it already > has its dissidents! Perhaps Han means people that insist in talking > about mathematics with some mathematicians from a non-mathematical > point of view and without knowing mathematics? People that attack > mathematicians and even mathematics (go figure!) when someone dares to > point out some mathematical mistake in some nonsense that THEY say is > correct IN SPITE of evidence in contrary? One cannot speak of correct with a mathematics that is a non-discipline and gives non-discplinary answers to ill-posed questions like this one: http://huizen.dto.tudelft.nl/deBruijn/grondig/natural.htm#bv Zero balls at noon? Carl Friedrich Gauss would have turned in his grave. Han de Bruijn
From: Dik T. Winter on 4 Oct 2006 08:17 In article <gbCUg.40$LU2.1(a)tornado.rdc-kc.rr.com> "Poker Joker" <Poker(a)wi.rr.com> writes: > "Dik T. Winter" <Dik.Winter(a)cwi.nl> wrote in message > news:J6FIqp.Cr6(a)cwi.nl... .... > > > I assume you accept this proof that there are no complete lists > > > of reals: > > > > > > Let r be a real number between 0 and 1. Let r_n denote the nth digit > > > in r's decimal expansion. Let r_n = 5 if r_n = 4, otherwise let r_n = > > > 4. > > > r isn't on any list of reals. Therefore there isn't a complete list of > > > reals. > > > > There is no r that satisfies that condition. > > That's how the number from step #2 is defined when the input is > all the reals. So we conclude that the number from step #2 is ill-defined. That is not how the number from step #2 is defined. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Dik T. Winter on 4 Oct 2006 08:24 In article <3076a$45236def$82a1e228$13750(a)news2.tudelft.nl> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > Albrecht wrote: > > > The idea of "all infinite many objects" in any sense is > > self-contradicting. There is no "all" of infinite many things. > > Bravo! Another mathematician (?) who cares about disciplinary thinking. Not a mathematician. I would think a Dipl.-Ing. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Tonico on 4 Oct 2006 08:40 Han de Bruijn wrote: > Tonico wrote: > > > Han de Bruijn ha escrito: > > > >>Wishful thinking on the part of William Hughes. A simple Google search > >>will reveal that the army of 'sci.math' dissidents is steadily growing. > > > > ************************************************** > > Zaas! Dissidents...from sci.math???? Didn't know somebody already > > formed a political or social or economical or > > whatever-that-isn't-science group called sci.math, and that it already > > has its dissidents! Perhaps Han means people that insist in talking > > about mathematics with some mathematicians from a non-mathematical > > point of view and without knowing mathematics? People that attack > > mathematicians and even mathematics (go figure!) when someone dares to > > point out some mathematical mistake in some nonsense that THEY say is > > correct IN SPITE of evidence in contrary? > > One cannot speak of correct with a mathematics that is a non-discipline > and gives non-discplinary answers to ill-posed questions like this one: > > http://huizen.dto.tudelft.nl/deBruijn/grondig/natural.htm#bv > > Zero balls at noon? Carl Friedrich Gauss would have turned in his grave. > > Han de Bruijn ************************************************** For what we know, I think dead people don't turn in their grave, or anywhere else for that matter. I agree though that the balls-vase-noon is a question ill-posed but with possibilities to be pretty interesting and deep into understanding some aspects of infinity and stuff. I'd rather pose the next thinker. Supose X is a person that never dies, and when he's 50,000 years old he begins writing his autobiography in a rather peculiar way: every day after his 50,000-th birthday he writes down one day of his life, beginning with his first day of life. The question is: does X write down ALL the days of his life in this autobiography? Pay attention: I am not asking whether there will ever be a book containing all the days of X's life, but rather whether there will exist some pages written by X describing the events of some given day of his life, for EVERY singled out day of X's life...? Of course, the above story is very similar to the one about the hotel in space witrh infinite rooms in it, etc. Regards Tonio Ps. BTWm abiut the balls-vase matter, I think the best answer is the one that said that noon, as we know it, is never reached according to the spirit of the question.
From: georgie on 4 Oct 2006 08:52
David R Tribble wrote: > Ross A. Finlayson wrote: > > Joker, and I've told people this before, please try and ignore Virgil. > > Why not ignore Poker Joker? At least Virgil knows set theory. > > Virgil, you really ought to refrain from feeding the trolls. > Their responses are only cluttering up the newsgroup. Virgil is obviously the troll. You are his side-kick. |