The Definition of Points
in [Math]
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From: Lester Zick on 1 Apr 2007 19:40 On Sat, 31 Mar 2007 18:47:45 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Fri, 30 Mar 2007 12:13:57 -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: >>>> >>>>>>> It's the same as Peano. >>>>>> Not it isn't, Tony. Cumulative addition doesn't produce straight lines >>>>>> or even colinear straight line segments. Some forty odd years ago at >>>>>> the Academy one of my engineering professors pointed out that just >>>>>> because there is a stasis across a boundary doesn't necessarily mean >>>>>> that there is no flow across the boundary only that the net flow back >>>>>> and forth is zero.I've always been impressed by the line of reasoning. >>>>> The question is whether adding an infinite number of finite segments >>>>> yields an infinite distance. >>>> I have no idea what you mean by "infinite" Tony. An unlimited number >>>> of line segments added together could just as easily produce a limited >>>> distance. >>>> >>>> ~v~~ >>> Not unless the vast majority are infinitesimal. >> >> No that isn't what I'm talking about. You seem to assume consecutive >> segments would have to be colinear and lie along a straight line. I've >> already tried to explain why this isn't so. They could all connect in >> completely different directions even though mathematikers commonly >> assume they somehow for some reason would very plolitely line up in >> one direction alone. Line segments are only connected by points, Tony. >> And their direction is not determined by those points because there is >> no definable slope at point intersections. >> > > >I'm sorry Lester. Perhaps I misunderstood. When you used the word >"added", I assumed you meant addition. That assumes a linear >construction. But, perhaps, you meant some other form of addition. >Addition is linear, as commonly understood... As is commonly pretended, Tony, and not however as is mechanically required. Modern mathematikers merely wish to assume the guise of geometry without the necessity of geometry. They just assume whatever they want because they think if they dress it up with enough mathspeak no one will notice the implicit assumptions of truth they're too lazy or stupid to conceal much less avoid. >>> If there is a nonzero >>> lower bound on the interval lengths, an unlimited number concatenated >>> produces unlimited distance. >> >> And if segments were all of equal finite size we could make a finite >> plane hexagon out them which would be quite limited in distance. >> >> ~v~~ > >Not exactly, but that's a complicated topic.... Sure exactly, Tony. And where exactly do all these exhalted self righteous modern mathematikers get off assuming whatever they feel like without so much as being able to demonstrate the truth of what they assume or even to define or identify what they assume as true? It looks to me like modern mathematikers collectively suffer from HBSE or Holy Bovine Spongiform Encephalopathy or Mad Sacred Cow Disease. ~v~~
From: Lester Zick on 1 Apr 2007 19:41 On Sat, 31 Mar 2007 19:50:10 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> 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~~ > >I've been dropping feathers and bowling balls out my window all >morning.... What do YOU think science is? Exactly what I said it was in E201: the demonstration of truth. That and nothing more or less. ~v~~
From: Lester Zick on 1 Apr 2007 19:42 On Sat, 31 Mar 2007 18:53:25 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Fri, 30 Mar 2007 12:24:12 -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: >>>> >>>>>>> Add 1 n >>>>>>> times to 0 and you get n. If n is infinite, then n is infinite. >>>>>> This is reasoning per say instead of per se. >>>>>> >>>>> Pro se, even. If the first natural is 1, then the nth is n, and if there >>>>> are n of them, there's an nth, and it's a member of the set. Just ask >>>>> Mueckenheim. >>>> Pro se means for yourself and not for itself. >>> In my own behalf, yes. >>> >>>> I don't have much to do >>>> with Mueckenheim because he seems more interested in special pleading >>>> than universal truth. At least his assumptions of truth don't seem >>>> especially better or worse than any other assumptions of truth. >>>> >>>> ~v~~ >>> He has some valid points about the condition of the patient, but of >>> course he and I have different remedies. >> >> Some of which may prove deadly. >> >> ~v~~ > >Well, his mostly consist of amputation and leeches, but as long as he >sticks to the extremities, I don't think death is inevitable... > >Mine don't actually break anything, except for the leeches, and some >bones... Tell it to George Washington. I'm sure he'll be impressed. ~v~~
From: Lester Zick on 1 Apr 2007 19:45 On Sat, 31 Mar 2007 18:55:34 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >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? Nothing. I just consider their claims to virtue suspect. No more so than modern mathematikers and empirics but suspect nonetheless. ~v~~
From: Lester Zick on 1 Apr 2007 19:47
On 31 Mar 2007 21:54:21 -0700, "Brian Chandler" <imaginatorium(a)despammed.com> wrote: >Do you want to try again? Not unless you can abbreviate it considerably. ~v~~ |