An uncountable countable set
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From: Virgil on 2 Oct 2006 15:40 In article <1159799981.773875.190290(a)b28g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Han de Bruijn schrieb: > > > > 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. > > You are right, but the illness does not begin with the vase, it beginns > already with the assumption that meaningful results could be obtained > under the premise that infinie sets like |N did actually exist. That opinion is a minority opinion.
From: Virgil on 2 Oct 2006 15:43 In article <45215a88(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > > Any true mathematics reserves decision until some number of iterations, > at least as a variable, has been declared. TO pontificating again on what "true mathematics" is? Those having seen some of TO's notions of what "true mathematics" is demur.
From: Virgil on 2 Oct 2006 15:48 In article <45215d2f(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Han de Bruijn wrote: > > stephen(a)nomail.com wrote: > >> 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. One can pose any gedanken one likes. If TO does not like to be able to tell one ball from another, he does not have to play the game, but he should not ever try to pull that in games of pool or billiards.
From: Han.deBruijn on 2 Oct 2006 15:54 mueckenh(a)rz.fh-augsburg.de schreef: > Han de Bruijn schrieb: > > > My mathematics says that it is an ill-posed question. And it doesn't > > give an answer to ill-posed questions. > > You are right, but the illness does not begin with the vase, it beginns > already with the assumption that meaningful results could be obtained > under the premise that infinie sets like |N did actually exist. Yes. That's why I launched the "Naturals Construction Set": http://groups.google.nl/group/sci.math/msg/13795822737a77ca?hl=nl& Han de Bruijn
From: David R Tribble on 2 Oct 2006 16:20
Tony Orlow wrote: >> For the sake of this argument, we can talk about infinite reals, of >> which infinite whole numbers are a subset. > David R Tribble wrote: >> What are these "infinite reals" and "infinite whole numbers" that you >> speak of so much? > Tony Orlow wrote: >> The very same, with no restriction of finiteness. Any T-riffic number >> has successor. :) > David R Tribble wrote: >> It's sporting of you to drop the requirement that all the naturals in N >> have to be finite, but since all of them are, it's meaningless to say >> "with no restriction of finiteness". That's kind of like saying N >> contains all naturals "with no restriction of non-integer values". >> I can say that, but it does not change the fact that all the members >> of N are integers. > Tony Orlow wrote: > Is the successor to ...11110000 not equal to ...11110001? I don't know - how are you defining those numbers? Even if it is (or is not), what does it have to do with the finite naturals? Are you saying that those "infinite naturals" are somehow successors to the finite naturals? How? David R Tribble wrote: >> So I ask again, where are those infinite naturals and reals you keep >> talking about? It's obvious they are not in N. > Tony Orlow wrote: > [No] it's not. Every member of N has a finite successor. Can you prove that your "infinite naturals" are members of N? |