The Definition of Points
in [Math]
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From: Lester Zick on 31 Mar 2007 19:55 On Fri, 30 Mar 2007 12:22:30 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>>> Finite addition never produces infinites in magnitude any more than >>>> bisection produces infinitesimals in magnitude. It's the process which >>>> is infinite or infinitesimal and not the magnitude of results. Results >>>> of infinite addition or infinite bisection are always finite. >>>> >>>>> Wrong. >>>> Sure I'm wrong, Tony. Because you say so? >>>> >>> Because the results you toe up to only hold in the finite case. >> >> So what's the non finite case? And don't tell me that the non finite >> case is infinite because that's redundant and just tells us you claim >> there is a non finite case, Tony, and not what it is. >> > >If you define the infinite as any number greater than any finite number, >and you derive an inductive result that, say, f(x)=g(x) for all x >greater than some finite k, well, any infinite x is greater than k, and >so the proof should hold in that infinite case. Where the proof is that >f(x)>g(x), there needs to be further stipulation that lim(x->oo: >f(x)-g(x))>0, otherwise the proof is only valid for the finite case. >That's my rules for infinite-case inductive proof. It's post-Cantorian, >the foundation for IFR and N=S^L. :) > >>> You can >>> start with 0, or anything in the "finite" arena, the countable >>> neighborhood around 0, and if you add some infinite value a finite >>> number of times, or a finite value some infinite number of times, you're >>> going to get an infinite product. If your set is one of cumulative sets >>> of increments, like the naturals, then any infinite set is going to >>> count its way up to infinite values. >> >> Sure. If you have infinites to begin with you'll have infinites to >> talk about without having to talk about how the infinites you >> have to talk about got to be that way in the first place. >> >> ~v~~ > >Well sure, that's science. Declare a unit, then measure with it and >figure out the rules or measurement, right? I have no idea what you think science is, Tony. Declare what and then measure what and figure out the rules of what, right, when you've got nothing better to do of an afternoon? ~v~~
From: Tony Orlow on 31 Mar 2007 19:55 Lester Zick wrote: > On 31 Mar 2007 10:02:17 -0700, "Brian Chandler" > <imaginatorium(a)despammed.com> wrote: > >> Tony Orlow wrote: >>> Brian Chandler wrote: >>>> Tony Orlow wrote: >>> Hi Imaginatorium - >> That's not my name - for some reason Google has consented to writing >> my name again. The Imaginatorium is my place of (self-)employment, > > And here I just assumed it was your place of self confinement. > >> so >> I am the Chief Imaginator, but you may call me Brian. > > Arguing imagination among mathematikers is like arguing virtue among > whores. > > ~v~~ So, what do you have against whores? 01oo
From: Mike Kelly on 31 Mar 2007 19:56 On 1 Apr, 00:36, Tony Orlow <t...(a)lightlink.com> wrote: > Lester Zick wrote: > > On Fri, 30 Mar 2007 12:10:12 -0500, Tony Orlow <t...(a)lightlink.com> > > wrote: > > >> Lester Zick wrote: > >>> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <t...(a)lightlink.com> > >>> wrote: > > >>>>>> Their size is finite for any finite number of subdivisions. > > >>>>> And it continues to be finite for any infinite number of subdivisions > >>>>> as well.The finitude of subdivisions isn't related to their number but > >>>>> to the mechanical nature of bisective subdivision. > > >>>> Only to a Zenoite. Once you have unmeasurable subintervals, you have > >>>> bisected a finite segment an unmeasurable number of times. > >>> Unmeasurable subintervals? Unmeasured subintervals perhaps. But not > >>> unmeasurable subintervals. > > >>> ~v~~ > >> Unmeasurable in the sense that they are nonzero but less than finite. > > > Then you'll have to explain how the trick is done unless what you're > > really trying to say is dr instead of points resulting from bisection. > > I still don't see any explanation for something "nonzero but less than > > finite". What is it you imagine lies between bisection and zero and > > how is it supposed to happen? So far you've only said 1/00 but that's > > just another way of making the same assertion in circular terms since > > you don't explain what 00 is except through reference to 00*0=1. > > > ~v~~ > > But, I do. > > I provide proof that there exists a count, a number, which is greater > than any finite "countable" number, for between any x and y, such that > x<y, exists a z such that x<z and z<y. No finite number of intermediate > points exhausts the points within [x,z], no finite number of > subdivisions. So, in that interval lie a number of points greater than > any finite number. Call |R in (0,1]| "Big'Un" or oo., and move on to the > next conclusion....each occupies how m,uch of that interval? > > 01oo So.. you (correctly) note that there are not a finite "number" of reals in [0,1]. You think this "proves" that there exists an infinite "number". Why? (And, what is your definition of "number")? -- mike.
From: Lester Zick on 31 Mar 2007 19:56 On Fri, 30 Mar 2007 12:25:24 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>>>> If n is >>>>> infinite, so is 2^n. If you actually perform an infinite number of >>>>> subdivisions, then you get actually infinitesimal subintervals. >>>> And if the process is infinitesimal subdivision every interval you get >>>> is infinitesimal per se because it's the result of a process of >>>> infinitesimal subdivision and not because its magnitude is >>>> infinitesimal as distinct from the process itself. >>> It's because it's the result of an actually infinite sequence of finite >>> subdivisions. >> >> And what pray tell is an "actually infinite sequence"? >> >>> One can also perform some infinite subdivision in some >>> finite step or so, but that's a little too hocus-pocus to prove. In the >>> meantime, we have at least potentially infinite sequences of >>> subdivisions, increments, hyperdimensionalities, or whatever... >> >> Sounds like you're guessing again, Tony. >> >> ~v~~ > >An actually infinite sequence is one where there exist two elements, one >of which is an infinite number of elements beyond the other. Which tells us what exactly, Tony, infinite sequences are infinite? ~v~~
From: Lester Zick on 31 Mar 2007 19:59
On 30 Mar 2007 21:17:38 -0700, "Brian Chandler" <imaginatorium(a)despammed.com> wrote: >> Under what definition of sequence? > >Oh come on... definition schmefinition. This is Tony's touchy-feely >statement of what he feels it would be for a sequence to be "actually >infinite". Actually. The same could be said for your touchy feely definitions, Brian. Six of one half dozen of the other. >You're just being disruptive, trying to inject some mathematics into >this stream of poetry... Mathematics? What mathematics did you have in mind exactly, Brian? SOAP operas? Zen? What pray tell? ~v~~ |