An uncountable countable set
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From: Virgil on 13 Oct 2006 16:00 In article <452fbf0e(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > So lets put them all in one minute earlier so they are all in before any > > have to be removed and each ball will be in for a longer time, and then > > remove them one at a time according to the original schedule. > > > > According to TO, putting them in earlier and taking them out as before > > leaves FEWER in the vase at noon, even though there is no change in > > removals. > > If you decouple the series of insertions with the series of removals, > each series having its own point of condensation (say, fill up to noon > and empty up to 12:01), then you have a different problem. So let us leave them coupled but merely change the coupling so that the nth ball is inserted, say , 1/2^n minutes before it is removed. Both the insertions and the removals are still all completed before noon, and it is obvious that the vase is empty at noon. > If the > series, which is a sequence, specifies that only one is removed for > every ten added, in alternation, then that creates a relation between > the insertions and removals that's so obvious, it really is weird that > it even merits discussion. When infinitely many are inserted and all of them removed, what is obvious to TO is false to logic.
From: Virgil on 13 Oct 2006 16:01 In article <452fbf62(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > 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. All of those inserted were removed.
From: Virgil on 13 Oct 2006 16:06 In article <452fc0c4(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > Does it prevent every ball from having a precise time before noon at > > which it is removed? Unless it does, it IS irrelevant. > > When does the last ball go in? Is it in by noon? How can there be a last ball inserted in a set of insertion-removal operations in which there is no last operation? TO is still hung up on his childish belief that unending sequences can have a last member. > > > > >>> The number of balls as a function of the number of insertion-removal > >>> operations completed certainly diverges, but how this prevents any > >>> specific ball from being removed before noon is not apparent, > >>> particularly when there is a specific rule determining when each ball is > >>> removed. > >> Yes, directly after ten others are inserted. The only way this could > >> result in an empty vase is if it had, at some point, -9 balls in the vase. > > > > There goes TO's phoney "last ball" argument again. > > If at most one ball is removed at any time, and the vase becomes empty, > then there is no other possibility but that there is a final ball > removed. However, that's impossible. So there must be another possibility, i.e., that there is no last ball.
From: Virgil on 13 Oct 2006 16:13 In article <452fc237(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <452ef7e7(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > >> No, Iv'v come around. I agree with you now. :) 0 has nothing whatsoever > >> to do with that sequence at all. Isn't that right? > > > > So TO concedes that the situation at noon has nothing to do with the > > sequence of numbers of balls at times before noon. > > Oh yeah, sure. In fact, it's given me a whole new perspective on life. > Nothing that's ever come before has anything to do with what's happening > or will happen. Every moment is an unconnected point, and there is no > continuity to the universe. It is supposing that occurrences in the mind's eye of mathematics are bound by the same constriants as occurrences in the physical world that produces those paradoxes. > I thought science made sense, but now I see > it's all an illusion, and that infinite things can appear or disappear > at will. Thanks for enlightening me. I also now believe in spontaneous > generation, divine creation, phlogiston, the forgiveness of the sin of > being innocent, The American Way, AMWAY, Gee Dubya, and Transfinitology. > I'm looking for funding to start The Transfinitological Seminary and > Sugar Shack Maple Museum. How much can I count you in for? To has clearly lost what little mind he once had through his inability to see the difference between the physical world and the world of the imagination.
From: Virgil on 13 Oct 2006 16:19
In article <452fc7c2(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > > I know that at no time have all the balls previous inserted been > removed, but only 1/9th of them, since 1 is removed for every 10 > inserted. What is the flaw in that logic? At no time BEFORE NOON have all the balls been removed. Since in the original statement of the problem, one was given the precise time before noon for removal of every ball that was to be inserted, by noon it does not matter a whit how long the ball was the vase. |