An uncountable countable set
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From: Virgil on 26 Oct 2006 17:32 In article <4540fa4b(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > stephen(a)nomail.com wrote: > > Tony Orlow <tony(a)lightlink.com> wrote: > >> It would still be inductively provable in my system that IN=OUT*10. > > > > So you actually think that there exists an integer n such that > > -1/(2^floor(n/10)) < 0 > > but > > -1/(2^n) >= 0 > > ? > > > > What might that integer be? > > > > Stephen > > > > How do you glean that from what I said? Your "largest finite" arguments > are very boring. TO's "largest integer" assumptions are even more so. They make him look even more foolish that usual. Which is quite an acheivement.
From: stephen on 26 Oct 2006 17:40 David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > stephen(a)nomail.com wrote: >> David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >> > The vase problem violates Tony's mental picture of a vase filling with >> > water. If we are steadily adding more water than is draining out, how >> > can all the water go poof at noon? Mental pictures are very useful, but >> > sometimes you have to modify your mental picture to match the >> > mathematics. Of course, when doing physics, we modify our mathematics to >> > match the experiment, but the vase problem originates in mathematics >> > land, so you should modify your mental picture to match the mathematics. >> >> As someone else has pointed out, the "balls" and "vase" >> are just an attempt to make this sound like a physical problem, >> which it clearly is not, because you cannot physically move >> an infinite number of balls in a finite time. It is just >> a distraction. As you say, the problem originates in mathematics. >> Any attempt to impose physical constraints on inherently unphysical >> problem is just silly. >> >> The problem could have been worded as follows: >> >> Let IN = { n | -1/(2^floor(n/10) < 0 } >> Let OUT = { n | -1/(2^n) } > I think you meant > Let OUT = { n | -1/(2^n) < 0 } >> What is | IN - OUT | ? >> >> But that would not cause any fuss at all. > I wonder. Does anyone reading this think | IN - OUT | <> 0? Tony does. Stephen
From: David Marcus on 26 Oct 2006 18:17 MoeBlee wrote: > Tony Orlow wrote: << snip >> > This is stupid for me to even be trying to talk to you about this. You > need to read and UNDERSTAND that damn first chapter in his book that > you're skipping. (And you'd understand it MUCH more easily if you first > read a book on mathematical logic and one on set theory). Otherwise, > you are oblivous to the BASIS of what he's doing. Sheesh. I admit that > I haven't read Robinson's original work, but at least I have > familiarized myself with well written summaries such as in Enderton's > book. And there is no way in heck that you're going to understand any > of this without getting a good basic understanding of the mathematical > logic and set theory that are the context and basis. I think it is too much for someone to learn on their own (unless they have quite a bit of mathematical maturity). Going to school is probably required. -- David Marcus
From: David Marcus on 26 Oct 2006 18:27 Virgil wrote: > In article <4540d217(a)news2.lightlink.com>,Tony Orlow <tony(a)lightlink.com> wrote: > > > Noon does not exist in the experiment, or else you have infinitely > > numbered balls. > > It is specifically mentioned in the experiment as the base time from > which all actions are determined, so that if it does not exist then none > of the actions can occur. > > If there is no noon then there can be no one minute before noon at which > the first ball is inserted, so the vase is frozen in a state of > emptiness. That's a good point. > > Like something occurring in time without at least a moment in which it > > occurred. > > In the physical world, nothing happens instantaneously. In the > mathematical world, pretty much everything does. > > In the mathematical world of the experiment, the balls move in and out > of the vase instantaneously, and must be allowed to do so or the > experiment cannot be performed at all. > > So either things can happen instantaneously or the experiment impossible. > > If TO allows a finite change of number of balls in the vase to occur > instantaneously, what is so difficult about allowing an "infinite" > change in the number of balls to occur instantaneously? That's another good point. -- David Marcus
From: Lester Zick on 26 Oct 2006 18:29
On 26 Oct 2006 11:37:06 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >Ross A. Finlayson wrote: >> Please identify something you see as incorrect or don't understand. > >What's the point? People have been pointing out your incorrect >statements for years. You just sail right past every time. > >So really think you are correct and that you make sense? So you really think you are correct and make sense, Moe? >It must be nice. Well tell us how it makes you feel. ~v~~ |