An uncountable countable set
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From: Lester Zick on 28 Oct 2006 15:27 On 27 Oct 2006 18:35:46 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >Tony Orlow wrote: >> Yes, Lester, your retorts ar very witty, and sometimes quite to the >> point, but not usually. But, always sharp. > >Not only is Orlow oblivious to logic and ignorant of mathematics, but >he's also prone to mistake the dull grunts of the likes of Lester Zick >for wit. Aw, poor baby. Sour grapes are the best kind, Moe. ~v~~
From: Lester Zick on 28 Oct 2006 15:29 On Fri, 27 Oct 2006 20:09:37 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Fri, 27 Oct 2006 01:37:04 -0400, David Marcus >> <DavidMarcus(a)alumdotmit.edu> wrote: >> >> [. . .] >> >>> It is interesting that when we try to ask Tony a question that doesn't >>> mention balls or vases or time, his answer involves balls, vases, and >>> time. I'm afraid to ask what 1 + 1 is because the answer might be "noon >>> doesn't exist". >> >> So if the definition for "1+1" entails "1(x)+1(x)" "balls" don't lie >> in the "domain of discourse" for "1+1"? Curious to say the least. >> >> ~v~~ > >1+1=2, of course, and noon doesn't exist. I think that's what David >wants to hear. It makes him feel good. :) I suspect the appropriate "domain of discourse" for David's balls is "in a vise". ~v~~
From: David Marcus on 28 Oct 2006 15:29 Tony Orlow wrote: > David Marcus wrote: > > Let me recap the discussion: Stephen suggested the following problem > > (which may or may not have some relationship to any other problem that > > anyone has ever considered): > > > > Define the following sets of natural numbers. > > > > IN = { n | -1/(2^floor(n/10)) < 0 }, > > OUT = { n | -1/(2^n) < 0 }. > > > > What is |IN\OUT|? > > > > Stephen suggested that this problem would "not cause any fuss at all", > > i.e., everyone would agree what the answer is. In reply, you wrote, "It > > would still be inductively provable in my system that IN=OUT*10." We all > > took this to mean that you disagreed that |IN\OUT| = 0. Now, you seem to > > be saying that you agree that |IN\OUT| = 0. > > > > Care to clear up this confusion? > > No, I don't care, but I'll do it anyway. :) Just kidding. Of course I > care, or I wouldn't waste my time. > > I am beginning to realize just how much trouble the axiom of > extensionality is causing here. That is what you're using, here, no? The > sets are "equal" because they contain the same elements. That gives no > measure of how the sets compare at any given point in their production. > Sets as sets are considered static and complete. However, when talking > about processes of adding and removing elements, the sets are not > static, but changing with each event. When speaking about what is in the > set at time t, use a function for that sum on t, assume t is continuous, > and check the limit as t->0. Then you won't run into silly paradoxes and > unicorns. There is a lot of stuff in there. Let's go one step at a time. I believe that one thing you are saying is this: |IN\OUT| = 0, but defining IN and OUT and looking at |IN\OUT| is not the correct translation of the balls and vase problem into Mathematics. Do you agree with this statement? -- David Marcus
From: Lester Zick on 28 Oct 2006 15:31 On 27 Oct 2006 16:20:26 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >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. "Modern math set analytical techniques" and "playtime" are in the same "domain of discourse". ~v~~
From: Tony Orlow on 28 Oct 2006 15:34
Randy Poe wrote: > Tony Orlow wrote: >> Virgil wrote: >>> 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? >> By the mechanism of unfinishablility. > > But that's why I asked you a question about variables labelling > times yesterday, when noon clearly occurred. The experiment occurred in [-1,0). Talk of time outside that range is irrelevant. Times before that are imaginary, and times after that are infinite. Only finite times change anything, so if something changes, it's at a finite, negative time. > > I can define a list of times t_n = noon yesterday - 1/n seconds, > for all n=1, 2, 3, ... Are there balls in the vase for t<-1? No. > > Clearly this list of times has no end. But didn't noon happen? Nothing happened at noon to empty the vase, and your desired miracle of emptiness did not happen before noon, so it had not occurred by noon, so it was not the case that the vase was empty then, at noon. Comprende? Ay Que prungisimo! > > How does my list affect the existence of noon yesterday? It's > unfinishable. Why don't your time-stopping rules work retroactively? > What's different about this set of times t_n and the set of times > in the balls-and-vase problem? Why does assigning these labels > to times yesterday not affect anything, but if I assign those > labels today, it stops time? > > - Randy > Why, oh why, do the constraints of the problem have to matter? Why, oh why, must we alway mean a continuum when we call something continuous, when I want to declare a discontinuity at convenient places like 0? Why can't we specify what happens at every moment y between x and z, but that something totally different is the case at z, without anything changing it? Why, oh why, why don't my labels matter? I'm not really sure how to answer this, again..... TOny |