An uncountable countable set
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From: Ross A. Finlayson on 13 Oct 2006 05:10 Virgil wrote: > In article <e5389$452f434a$82a1e228$30886(a)news2.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > Alan Morgan wrote: > > > > > In article <452e8c2a(a)news2.lightlink.com>, > > > Tony Orlow <tony(a)lightlink.com> wrote: > > > > >>What is sum(n=1->oo: 9)? > > > > > > I think you actually mean, what is 10-1+10-1+10-1.... > > > > > > It was recognized long before Cantor that there isn't a simple answer to > > > that question. > > > > It was recognized long before Cantor that there isn't an answer at all > > to a meaningless question. > > > > Han de Bruijn > > But there was then, and remains today, wide disagreement on exactly > which questions are meaningless. > > And it is not an issue on which I would trust HdB's judgement. Virgil is liar, AND coward. Is that so wrong? Then you might as well expect there's a better mathematical theory, Ross: "the finest product of the public school system" Ross
From: Han de Bruijn on 13 Oct 2006 05:23 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. >>Thus the end result is _undefined_. > > Not in logic. I rest my case (-: what does that phrase mean, BTW?) Han de Bruijn
From: Ross A. Finlayson on 13 Oct 2006 05:24 Ross A. Finlayson wrote: > Virgil wrote: > > > > So that TO says that at noon, after a particular ball, like number 15, > > has been removed, it may not be distinguishable whether ball 15 is in > > the vase of not? > > > > What a weird world TO lives in. > > And you don't? > Ha ha ha ha ha ha. Oh, I laugh. Ross -- --- "I see that Ross has succeeded in altering the language of sci.math. It's enough to make one weep." - R. Poe
From: Han de Bruijn on 13 Oct 2006 05:26 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. Han de Bruijn
From: Han de Bruijn on 13 Oct 2006 05:29
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. Han de Bruijn |