An uncountable countable set
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From: Virgil on 27 Oct 2006 19:08 In article <454238e4(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > > I think it is an answer. Just to be sure, please confirm that you agree > > that, with the definitions above, V(0) = 0. Is that correct? > > > > Sure, all finite balls are gone at noon. And in any system compatible with ZF or NBG there aren't any others.
From: MoeBlee on 27 Oct 2006 19:09 Lester Zick wrote: > Ah, Moe, truth is often a nuisance. Then you're as much of a nuisance as is a cool breeze on a sunny spring day, as a cleansing and quenching rain that ends a drought, as a magnificent symphony orchestra heard in an amphitheatre of impeccable acoustics. Moe Blee
From: MoeBlee on 27 Oct 2006 19:20 Lester Zick wrote: MoeBlee wrote: > >Please stop mangling what I've said and then representing your mangled > >interpretations as if they are what I said. > > I will if you'll just stop doubletalking, Moe. No, you'll just keep doing it until, like a child pestering to play "peek-a-boo", constantly tugging on the coats of adults, you tire of your own silly game. MoeBlee
From: Virgil on 27 Oct 2006 19:24 In article <454286b7(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > imaginatorium(a)despammed.com wrote: > > Forgive me if I blunder in on Chas's carefully constructed argument, > > but... > > > > Here's something I don't understand. I believe, Tony, that you think > > that if every one of these pofnat-labelled balls is inserted one minute > > earlier (so *informally*, instead of a "sliver" tapering to zero width, > > we have an endless boomerang shape, with the width tending to 1 as you > > go ever up the y-direction), then at noon no balls are left. Presumably > > because once all the balls are IN (at 11:59), there is only removal, > > tick, tick, tick, ... and all are gone at noon. But why doesn't this > > stuff about "noon being incompatible" apply here too? Is there a > > *principled* way in which you determine which arguments apply at > > particular points? (I'm sure it appears to most non-cranks here that > > there isn't.) > > That's very simple, Brian. The limit of balls as n->noon is 0. That's > not the case in the original problem. So that TO is arguing that the later balls are put in, the more will be there at noon? But that also creates contradictions. Let us delay the insertion of ball number n, which is to be removed at 1/n minutes before noon until (1/n + 1/(n-1))/2 minutes before noon, but remove it as originally scheduled. Then at any time before noon there will be either 0 or 1 balls in the vase, and these values will alternate. If TO's logic were consistent, then at noon there would have to be half a ball in the vase, but what number, or fraction of a number, it would bear, or what numbers it would share, is not readily apparent. > > Which of my statements above do you find objectionable, and why? That > would be helpful to know. Among others, the notion that balls are created at noon out of thin air to fill the "vacuum" that having every ball removed before noon seems to create in TO's head.
From: Virgil on 27 Oct 2006 19:26
In article <454286e8(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > stephen(a)nomail.com wrote: > > David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > >> Tony Orlow wrote: > >>> David Marcus wrote: > >>>> Your question "Is there a smallest infinite number?" lacks context. You > >>>> need to state what "numbers" you are considering. Lots of things can be > >>>> constructed/defined that people refer to as "numbers". However, these > >>>> "numbers" differ in many details. If you assume that all subjects that > >>>> use the word "number" are talking about the same thing, then it is > >>>> hardly surprising that you would become confused. > >>> I don't consider transfinite "numbers" to be real numbers at all. I'm > >>> not interested in that nonsense, to be honest. I see it as a dead end. > >>> > >>> If there is a definition for "number" in general, and for "infinite", > >>> then there cannot both be a smallest infinite number and not be. > > > >> A moot point, since there is no definition for "'number' in general", as > >> I just said. > > > >> -- > >> David Marcus > > > > A very simple example is that there exists a smallest positive > > non-zero integer, but there does not exist a smallest positive > > non-zero real. If someone were to ask "does there exist a smallest > > positive non-zero number?", the answer depends on what sort > > of "numbers" you are talking about. > > > > Stephen > > Like, perhaps, the Finlayson Numbers? :) Any set of numbers whose properties are known. Are the properties of "Finlayson Numbers" known to anyone except Ross himself? |