The Definition of Points
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From: Lester Zick on 17 Mar 2007 19:40 On Sat, 17 Mar 2007 18:24:48 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: ><nonsense(a)unsettled.com> wrote in message >news:b71c5$45fc1f22$4fe72e0$21877(a)DIALUPUSA.NET... >> SucMucPaProlij wrote: >> >>>>You can develop geometry based purely on real numbers and sets. You need not >>>>assume any geometrical notions to do the thing. One of the triumphs of >>>>mathematics in the modern era was to make geometry the child of analysis. >>>> >>> >>> >>> And it means that lines, planes and points are defined in geometry. >>> Make up your mind, Bob! >> >> No they're not. "The locus of all points...." >> >> >> > >You can't define points and lines with numbers and sets? >Try it. It is not hard. Oh goodie. I can hardly wait. ~v~~
From: Lester Zick on 17 Mar 2007 19:41 On Sat, 17 Mar 2007 13:54:18 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >SucMucPaProlij wrote: >> >> >> You can't define points and lines with numbers and sets? >> Try it. It is not hard. > >Points (in n-dimesnsional space) are ordered n-tuples of real numbers. That's really helpful. ~v~~
From: SucMucPaProlij on 17 Mar 2007 19:43 "Lester Zick" <dontbother(a)nowhere.net> wrote in message news:ilrov2l07utt9j1ma26lm7stptkh28a9rg(a)4ax.com... > On 17 Mar 2007 09:40:22 -0700, "Randy Poe" <poespam-trap(a)yahoo.com> > wrote: > >>Every abstract concept exists as a concept. What does the >>size of the universe have to do with that? They don't >>take up any space. > > What does the space concepts take up have to do with their truth? > Every idea/concept/definition/axiom must be expressed in some physical form - it must be formulated. You can't express concept that has more elements/parts/whatever than number of atoms in universe. If you have concept that takes all but one atom then you can't tell if it is true or not - you don't have enough resources to do so but you still have one extra atom that you probably can't use for anything :)))))
From: Bob Kolker on 17 Mar 2007 20:06 Tony Orlow wrote:> > Except that linear order (trichotomy) and continuity are inherent in R. > Those may be considered geometric properties. They can be defined in a purely analytic and algebraic manner starting with the Peano axioms. While linear order is suggestive of geometric notions, one can define such order without any geometric content whatsoever. The order of the postive integers is more temporal than spatial. Fist comes an integer -then- comes its successor. Etc. Etc. Bob Kolker
From: Wolf on 17 Mar 2007 22:40
SucMucPaProlij wrote: > "Bob Kolker" <nowhere(a)nowhere.com> wrote in message > news:5629arF26ac36U1(a)mid.individual.net... >> SucMucPaProlij wrote: >>> I don't want you to expect too much because this is not mathematical proof, >>> it is philosophical proof (or discussion). This is just the way how I explain >>> things to myself. >> If it ain't mathematics and it ain't physics, it is bullshit. Philsophy, by >> and large, is academic style bullshit. >> > > Isaak Newton: Philosophiae Naturalis Principia Mathematica > > or "academic style bullshit" > > > Think first, reply latter, Bob! > > In those days, "philosophy" meant what we now mean by "science." -- Wolf "Don't believe everything you think." (Maxine) |