An uncountable countable set
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From: Virgil on 29 Sep 2006 15:40 In article <451d5f77(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <451baaa0$1(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Virgil wrote: > >>> In article <451b3296(a)news2.lightlink.com>, > >>> Tony Orlow <tony(a)lightlink.com> wrote: > >>> > >>>> Randy Poe wrote: > >>>>> Tony Orlow wrote: > >>>> You must have been a strange 10 year old, like that kid > >>>> down the block that used to pull the legs off of roaches. > >>> Only those that looked like TO. > >>> > >>>>>>> So the reason I don't say it's full "an infinitesimal time > >>>>>>> before noon" or "some other time before noon" is that > >>>>>>> I don't say it's full. > >>>>>> But, you do say it's full or empty, right? > >>> One can easily say that it is empty at any time at which every ball > >>> that was put in has been taken out again. > >>> > >>> Does TO suggest that at any time after noon there is any ball that was > >>> put in that was not also taken out? > >> Yes, at any given time 9/10 of the balls inserted remain. > > > > TO's "yes" is a claim that some ball does not get removed. > > Name one ball, by number, which does not get removed, TO. > > > >>>> If you say it empties, then you would agree that it either fills or it > >>>> empties. When does it empty? You say, not before noon. You also say > >>>> this does not occur at noon, but after noon there are no balls left. So > >>>> when does this occur? > >>> When every ball that was put in has also been taken out again. > >> At noon or before noon? You're skirting the issue. > > > > To is the one skirting the issue by claiming that some balls remain but > > being unable to name any of them. > > Your labels are a bunch of hooey. Not being able to name which molecules > of water remain in an ocean being filled at 10 liter/min and emptied at > 1 liter/min has nothing to do with whether it ever empties. You're > playing voodoo. The game started with labeled balls. If TO wants to play it with different rules, say with unlabeled balls, then one has a different game that may end differently, but playing by the original rules of the original game, the vase ends empty.
From: Virgil on 29 Sep 2006 15:43 In article <451d5ff7$1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <451babf8(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> It's possible because no distinction is currently made between countable > >> infinities, even to the point where a set dense in the reals like the > >> rationals is considered equal to a set sparse in the reals like the > >> naturals. > > > > TO would require that changing the order relation on a set changes its > > size as if reordering the naturals into a dense set, like the rationals, > > would somehow make more of them > > The order of everything on the real line is quantity. The order is an order relation only, nothing more. > > Virgil would require that the real line have a different length for > every different infinite set he embedded on the line, so that they could > all be the same size sets. If one reorders the real line or any other ordered set, then the "distance" between members of that newly ordered set depends of the new ordering. It's like wearing uniforms in school.
From: Virgil on 29 Sep 2006 15:49 In article <451d6037(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <451bac34(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >>>> If the vase is empty at noon, but not before, how can that not be the > >>>> moment that it becomes empty? > >>> Saying that it is empty is quite different from saying anything about a > >>> "last ball". andy does not deny that the vase becomes empty, he just > >>> does not say anything about any "last ball out". > >> Does that answer the question of **when** this occurs? Of course not. > > > > It does answer the question of "whether" it occurs. "When" is of lesser > > importance. > > So, you have no answer. And so it's not important. I see. When have all the balls, whether removed or not, all been inserted? That is the time at which all have also been removed, as no ball can be removed before its insertion nor after all have been inserted. Except for the first 10 balls, each insertion follow a removal and with no exceptions each removal follows an insertion.
From: Virgil on 29 Sep 2006 15:50 In article <451d62fc(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <451bafc9(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Han de Bruijn wrote: > >>> Virgil wrote: > >>> > >>>> In article <d12a9$451b74ad$82a1e228$6053(a)news1.tudelft.nl>, > >>>> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>>> > >>>>> Randy Poe wrote, about the Balls in a Vase problem: > >>>>> > >>>>>> It definitely empties, since every ball you put in is > >>>>>> later taken out. > >>>>> And _that_ individual calls himself a physicist? > >>>> Does Han claim that there is any ball put in that is not taken out? > >>> Nonsense question. Noon doesn't exist in this problem. > >>> > >>> Han de Bruijn > >>> > >> That's the question I am trying to pin down. If noon exists, that's when > >> the vase supposedly empties, since it doesn't do before then. If the > >> limit doesn't "actually occur", then vase never empties (not that it > >> would anyway). > > > > If the vase were not empty after noon, someone ought to be able to say > > which balls were in it. Since no one will say, I will continue to > > maintain that after noon the vase is empty. > > Since it is impossible to say how many iterations are performed by noon, > it's impossible to number the balls. If balls 1 through n are > inserted, balls n/10+1 through n will remain. Except that they don't.
From: Virgil on 29 Sep 2006 15:56
In article <451d6324(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <451be86a(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > > > >>> What is the number of the ball which, when removed, > >>> makes the vase empty? > >>> > >> There is no such number, since for each ball n removed, balls n+1 > >> through balls n*10 remain. I have maintained throughout that, despite > >> your "labeling schemes", 9/10 of the balls remain, if you add 10 and > >> remove 1 repeatedly. It is precisely like adding 10 gallons and removing > >> 1 per minute. The ocean will never empty. Think measure. > > > > So which balls are left after noon, TO? > > If n balls are inserted, balls n/10+1 through n remain. Supose we put the balls removed from the vase into an initially empty urn. Is ball 1 put into the urn by noon? Yes! If ball n is put into the urn by noon, is ball n+1 also put into the urn by noon? Yes! Conclusion: By induction all the numbered balls are put into the urn before noon. Sop TO must be out somewhere making unnumbered balls and sneaking them into the vase when no one is looking, at least if there are to be any balls left in the vase and not moved to the urn. |