An uncountable countable set
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From: Virgil on 28 Sep 2006 14:09 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.
From: Virgil on 28 Sep 2006 14:15 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
From: Virgil on 28 Sep 2006 14:16 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.
From: Virgil on 28 Sep 2006 14:18 In article <451baf65(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Han de Bruijn wrote: > > Randy Poe wrote: > > > >> What I would say about emptying is that the vase is empty > >> at noon, but there is no identifiable time before noon at which > >> we can say "the last ball was taken out then". > >> > >> At any time before noon, there are balls in the vase. There > >> is no time we can say "there goes the last ball out" since there > >> is no last ball in. > > > > What I would say about emptying is that the balls must have been filled > > with liquor. And that you must have swallowed them all before you wrote > > this post. > > > > Han de Bruijn > > > > That's why Randy has that vase-like physique. It's from the distended liver! Whereas TO is just naturally pear-shaped.
From: Virgil on 28 Sep 2006 14:19
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. |