An uncountable countable set
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From: Virgil on 27 Oct 2006 16:41 In article <45421a34(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > David Marcus wrote: > > So, "noon exists" in this case, even though nothing happens at noon. > > Not really Yes really.
From: Virgil on 27 Oct 2006 16:46 In article <45421ba8(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > > On the surface, you math appears correct, but that doesn't mend the > obvious contradiction in having an event occur in a time continuum > without occupying at least one moment. It doesn't explain how a > divergent sum converges to 0. Basically, what you prove, if V(0)=0, is > that all finite naturals are removed by noon. I never disagreed with > that. However, to actually reach noon requires infinite naturals. Where do these alleged infinite naturals come from? Then are certainly not available in the original gedankenexperiment, which takes place in a mathematical world compatible with ZF or NBG. They spring full-blown from TO's "intuition", which is hostile to all standard mathematics, and so irrelevant to all standard mathematics. And the gedankenexperiment occurs in standard mathematics.
From: Virgil on 27 Oct 2006 16:55 In article <4542201a(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > cbrown(a)cbrownsystems.com wrote: > > When you say "noon doesn't occur"; I think "he doesn't accept (1): by a > > time t, we mean a real number t" > > That doesn't mean t has to be able to assume ALL real numbers. The times > in [-1,0) are all real numbers. By what mechanism does TO propose to stop time? > > > > > When you say "if we always add more balls than we remove, the number of > > balls in the vase at time 0 is not 0", I think "he doesn't accept (8): > > if the numbers of balls in the vase is not 0, then there is a ball in > > the vase." > > No, I accept that. There is no time after t=-1 where there is no ball in > the vase. That is not the same thing at all, as it requires that some ball remain in the vase after it has been removed. > I didn't say that exactly. If 0 occurs, then all finite balls are gone, As those are the only balls that the gedankenexperiment allows, that means the vase is then empty. > but infinite balls have been inserted Where in the original gedankenexperiment is there any provision made for those alleged "infinite" balls? What TO does is decide what result he wants and then tries to bend the facts to fit. But it does not work. The only relevant question is "According to the rules of the gedankenexperiment , is each ball which is inserted into the vase before noon also removed from the vase before noon?" An affirmative answer confirms that the vase is empty at noon. A negative answer directly violates the conditions of the gedankenexperiment. So TO keeps violating the conditions of the gedankenexperiment.
From: Virgil on 27 Oct 2006 16:57 In article <45422275(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Ross A. Finlayson wrote: > > Tony Orlow wrote: > > > >> For what it's worth, and I know this doesn't add a lot of credibility to > >> Ross in your eyes, coming from me, but I think Ross has a genuine > >> intuition that isn't far off with respect to what's controversial in > >> modern math. Sure, he gets repetitive and I don't agree with everything > >> he says, but his cryptic "Well order the reals", which I actually > >> haven't seen too much of lately, is a direct reference to his EF > >> (Equivalence Function, yes?) between the naturals and the reals in > >> [0,1). The reals viewed as discrete infinitesimals map to the > >> hypernaturals, anyway, and his EF is a special case of my IFR. So, to > >> answer your question, I think Ross makes some sense. But, of course, > >> coming from me, that probably doesn't mean much. :) > >> > >> TOE-Knee > > > > Hi, > > > > What is this IFR, "inverse function rule"? I've heard you mention it. > > Is it just general EF? > > > > Ross > > > Hey Ross! > > The Inverse Function Rule uses infinite-case induction to finely order > infinite sets of reals mapped from a standard set, N. It is merely another delusion of TO's that such a rule means anything to anyone except TO.
From: Virgil on 27 Oct 2006 16:59
In article <45422318(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > The inverse mapping gives the number of elements over a given value > range, which can be applied to the entire set of reals, providing > intuitive results (like half as many events as naturals) for infinite > sets when that real range is considered constant. It is part of a dreamworld in which TO dreams that he is the new Cantor. |