The Definition of Points
in [Math]
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From: Lester Zick on 14 Mar 2007 01:54 On 13 Mar 2007 17:18:03 -0700, "Eric Gisse" <jowr.pi(a)gmail.com> wrote: >On Mar 13, 9:52 am, Lester Zick <dontbot...(a)nowhere.net> wrote: >> The Definition of Points >> ~v~~ >> >> In the swansong of modern math lines are composed of points. But then >> we must ask how points are defined? However I seem to recollect >> intersections of lines determine points. But if so then we are left to >> consider the rather peculiar proposition that lines are composed of >> the intersection of lines. Now I don't claim the foregoing definitions >> are circular. Only that the ratio of definitional logic to conclusions >> is a transcendental somewhere in the neighborhood of 3.14159 . . . >> >> ~v~~ > >Points, lines, etc aren't defined. Only their relations to eachother. So is the relation between points and lines is that lines are made up of points and is the relation between lines and points that the intersection of lines defines a point? ~v~~
From: Lester Zick on 14 Mar 2007 01:58 On 13 Mar 2007 18:17:55 -0700, "Tom Potter" <tdp1001(a)gmail.com> wrote: > >"Eric Gisse" <jowr.pi(a)gmail.com> wrote in message >news:1173831482.988051.220120(a)y66g2000hsf.googlegroups.com... >> On Mar 13, 9:52 am, Lester Zick <dontbot...(a)nowhere.net> wrote: >>> The Definition of Points >>> ~v~~ >>> >>> In the swansong of modern math lines are composed of points. But then >>> we must ask how points are defined? However I seem to recollect >>> intersections of lines determine points. But if so then we are left to >>> consider the rather peculiar proposition that lines are composed of >>> the intersection of lines. Now I don't claim the foregoing definitions >>> are circular. Only that the ratio of definitional logic to conclusions >>> is a transcendental somewhere in the neighborhood of 3.14159 . . . >>> >>> ~v~~ >> >> Points, lines, etc aren't defined. Only their relations to each other. > >Euclid's Elements > >Definition 1. >A point is that which has no part. > >Definition 2. >A line is breadthless length. > >Definition 3. >The ends of a line are points. > >Definition 4. >A straight line is a line which lies evenly with the points on >itself. > >Definition 5. >A surface is that which has length and breadth only. > >Etc. > >I suggest that the best definition of point >as far as physics is concerned, would be: >"A point is the intersection of orthogonal properties." > >In other words, >a physical point is where time, x,y, and z spaces, >charge and impedance are referenced. Fascinating. But are lines composed of points? The foregoing definitions are reasonable as far as they go however I see nothing in them that sheds light on this issue. ~v~~
From: Lester Zick on 14 Mar 2007 02:00 On Wed, 14 Mar 2007 01:23:33 GMT, Sam Wormley <swormley1(a)mchsi.com> wrote: >Tom Potter wrote: > >> Euclid's Elements >> >> Definition 1. >> A point is that which has no part. >> >> Definition 2. >> A line is breadthless length. >> >> Definition 3. >> The ends of a line are points. >> >> Definition 4. >> A straight line is a line which lies evenly with the points on >> itself. >> >> Definition 5. >> A surface is that which has length and breadth only. >> > > Hey Potter--That was a useful posting for a change! Certainly useful as far as it goes however not very useful for elucidating the basic question as to whether points compose lines. ~v~~
From: Eric Gisse on 14 Mar 2007 02:21 On Mar 13, 9:54 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > On 13 Mar 2007 17:18:03 -0700, "Eric Gisse" <jowr...(a)gmail.com> wrote: > > >On Mar 13, 9:52 am, Lester Zick <dontbot...(a)nowhere.net> wrote: > >> The Definition of Points > >> ~v~~ > > >> In the swansong of modern math lines are composed of points. But then > >> we must ask how points are defined? However I seem to recollect > >> intersections of lines determine points. But if so then we are left to > >> consider the rather peculiar proposition that lines are composed of > >> the intersection of lines. Now I don't claim the foregoing definitions > >> are circular. Only that the ratio of definitional logic to conclusions > >> is a transcendental somewhere in the neighborhood of 3.14159 . . . > > >> ~v~~ > > >Points, lines, etc aren't defined. Only their relations to eachother. > > So is the relation between points and lines is that lines are made up > of points and is the relation between lines and points that the > intersection of lines defines a point? No, it is more complicated than that. http://en.wikipedia.org/wiki/Hilbert's_axioms > > ~v~~
From: Bob Cain on 14 Mar 2007 02:28
The_Man wrote: > What do YOU produce, Mister Nick Ick? What have YOU accomplished? He's good at starting vanity threads to demonstrate his self proclaimed and self appreciated wit. He's a legend in his own mind. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |