The Definition of Points
in [Math]
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From: SucMucPaProlij on 14 Mar 2007 05:05 > > You don't have to accept anything. It might be nice however if you had > some tenable alternative to suggest. Are you suggesting lines are not > made up of points and the intersection of lines does not define a > point? Or are you suggesting we just ignore the problem because modern > mathematikers are too lazy or stupid to resolve it? > I think that you are just playing dumb. "Line is made of points" is not definition of line and modern mathematikers can resolve your questions. Intersection of lines can define a point and we both know it just as we both know that line is made of points. If you don't think that line is made of points then how do you explain the fact that two lines can have common point? If two lines are intersecting in a point is this point one part of both lines or is it created during intersectioning?
From: Bob Kolker on 14 Mar 2007 09:07 SucMucPaProlij wrote: > > Intersection of lines can define a point and we both know it just as we both > know that line is made of points. > > If you don't think that line is made of points then how do you explain the fact > that two lines can have common point? If two lines are intersecting in a point > is this point one part of both lines or is it created during intersectioning? Maybe he thinks there are objects other than points on lines. If so, they are not ever mentioned in any axiom system for Euclidean Geometry. Likwise for planar curves. L.Z. rejects the usual definition of a cirlce as a set of points on a plane a given distance (the radius) from a specified point (the center). If a circle does not consist of its points, what else besides points lie on the circle? If there are any such objects they are never mentioned in the axioms. Zick'w problem (among several problems he has) is that he simply does not comprehend what an axiomatic system is. He cannot comprehend the notion of undefined terms or objects whose only properties are given in the axioms. For example, whatever a point is, given two distinct points there is one and only one line (whatever a line is) containing them. Bob Kolker
From: SucMucPaProlij on 14 Mar 2007 09:23 "Bob Kolker" <nowhere(a)nowhere.com> wrote in message news:55qac4F24r2boU1(a)mid.individual.net... > SucMucPaProlij wrote: > >> >> Intersection of lines can define a point and we both know it just as we both >> know that line is made of points. >> >> If you don't think that line is made of points then how do you explain the >> fact that two lines can have common point? If two lines are intersecting in a >> point is this point one part of both lines or is it created during >> intersectioning? > > Maybe he thinks there are objects other than points on lines. If so, they are > not ever mentioned in any axiom system for Euclidean Geometry. > One can assume that there are some objects other than points but I don't think that anyone can prove that this objects are not points becouse you can't tell a difference between single point that stands alone and some imaginary object that is on a line. They both have the same simple characteristics (coordinates) and that is all they have. > Likwise for planar curves. L.Z. rejects the usual definition of a cirlce as a > set of points on a plane a given distance (the radius) from a specified point > (the center). If a circle does not consist of its points, what else besides > points lie on the circle? If there are any such objects they are never > mentioned in the axioms. > > Zick'w problem (among several problems he has) is that he simply does not > comprehend what an axiomatic system is. He cannot comprehend the notion of > undefined terms or objects whose only properties are given in the axioms. For > example, whatever a point is, given two distinct points there is one and only > one line (whatever a line is) containing them. > well, nobody is perfect...
From: Wolf on 14 Mar 2007 10:57 Lester Zick wrote: [...] > > Only because I learned to write before I learned to read. [...] Lester, I suggest you present yourself to the nearest experimental psychologist, and explain how you managed this trick.
From: Wolf on 14 Mar 2007 11:04
Eric Gisse wrote: > 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~~ > > Hey, Eric, you're actually trying to teach Zick something. IOW, you're assuming he really wants to know. But Zick doesn't want to be taught. To be taught would mean admitting that he doesn't know what he's talking about, or worse, that he cannot understand what you are explaining. For reasons we had better not examine to closely, Zick can't tolerate that admission. -- Wolf "Don't believe everything you think." (Maxine) |