An uncountable countable set
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From: Virgil on 13 Oct 2006 15:39 In article <257fc$452f5b13$82a1e228$14790(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <66a8$452f4298$82a1e228$30886(a)news2.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > >>Randy Poe wrote about the Balls in a Vase problem: > >> > >>>Tony Orlow wrote: > >> > >>>>Specifically, that for every ball removed, 10 are inserted. > >>> > >>>All of which are eventually removed. Every single one. > >> > >>All of which are eventually inserted. Every single one. > > > > None are reinserted after being removed but,each is removed after having > > been inserted, so that leaves them all outside the vase at noon. > > Huh! Then reverse the process: first remove 1, then insert 10. It must > be no problem in your "counter intuitive" mathematics to start with -1 > balls in that vase. My mathematics is only "counter-intuitive" where intuition and logic clash, and then it sides with logic. And -1 balls in a vase is counter-logic. Such numbers of balls must logically be naturals and -1 is not a natural. > > >>Thus the end result is _undefined_. > > > > Not in logic. > > I rest my case (-: what does that phrase mean, BTW?) It is a term from law. When one argues a case in court and finishes arguing, one says it. > > Han de Bruijn
From: Virgil on 13 Oct 2006 15:44 In article <9f4a$452f5bc7$82a1e228$14790(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > What bugs many people is that they cannot imagine discontinuous > > behavior in the physical world, so are unprepared to imagine it in the > > imaginary world in which this gedankenexperiment must take place. > > Not only that they can not imagine. There _is no_ such "discontinuous > behavior" in the physical world. That is something that HdB must accept purely on faith but cannot ever prove absolutely. I concur that there is no reason offhand to suppose that there is discontinuous behavior in the physical world, but I am a good deal less certain of its impossibility than HdB.
From: Virgil on 13 Oct 2006 15:47 In article <3df0f$452f5c6a$82a1e228$14790(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <9020$452f46c4$82a1e228$31963(a)news2.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > >>Virgil wrote about the Balls in a Vase problem: > >> > >>>Everything takes place before noon, so that by noon, it is all over and > >>>done with. > >> > >>Noon is never reached, because your concept of time is a fake. > > > > No one expects the experiment to take place anywhere except in the > > imagination, so that everything about it, including its time, is > > imaginary, but logic continues to hold even there, at least for > > mathematicians. And logic says that a ball removed from a vase is not > > later in the vase. > > Since your logic and the logic of others give contradictory results for > the same problem, logic alone is unreliable. If it were all the same logic based on the same assumptions, possibly, but the logic of others allows assumptions that my logic forbids. Within my logic, limited to the assumptions it allows, no contradictions occur, so there is no reason to suppose that my logic is unreliable.
From: Virgil on 13 Oct 2006 15:50 In article <452fbf62(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > >> which is supposed to be the limit of this > >> sequence? > > > > Why is it the limit of any sequence? > > And since the set of balls removed by noon includes every ball, how > > does TO come up with any balls still waiting to be removed at noon? > > You tell me how many were removed, and I'll tell you how many remain. Card(N) were removed including the first numbered ball and each successively numbered ball.
From: Virgil on 13 Oct 2006 15:53
In article <452fbe21(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <452ef411(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> The whole point of the Zeno machine is to conceive of completing this > >> infinite series of events, and yet, it compresses the vast majority of > >> events into a single moment at noon, making it impossible to distinguish > >> them. > > Actually, in either version of the original problem, NONE of the > > transactions take place AT noon. Each of them precedes noon. > > And, after each of those transactions, before noon, there is an > increased finite number of balls in the vase. So, it's nothing but > finite and growing before noon. Then, at noon.....what? The linear > growth implodes? It's true hogwash at its worst, Virgil, and you know it. Then how is it that in your analysis, by putting the balls in earlier, but taking them out at the original times, one ends with fewer in the vase? Now THAT is prime hogwash. |