The Definition of Points
in [Math]
|
Prev: Guide to presenting Lemma, Theorems and Definitions
Next: Density of the set of all zeroes of a function with givenproperties
From: Lester Zick on 13 Mar 2007 18:13 On Tue, 13 Mar 2007 18:43:09 GMT, Sam Wormley <swormley1(a)mchsi.com> wrote: >Lester Zick 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~~ > > Point > http://mathworld.wolfram.com/Point.html > > A point 0-dimensional mathematical object, which can be specified in > n-dimensional space using n coordinates. Although the notion of a point > is intuitively rather clear, the mathematical machinery used to deal > with points and point-like objects can be surprisingly slippery. This > difficulty was encountered by none other than Euclid himself who, in > his Elements, gave the vague definition of a point as "that which has > no part." Sure, Sam. I understand that there are things we call points which have no exhaustive definition. However my point is the contention of mathematikers that lines are made up of points is untenable if lines are required to define points through their intersection.It's vacuous. ~v~~
From: Lester Zick on 13 Mar 2007 18:17 On 13 Mar 2007 12:08:57 -0700, "Douglas Eagleson" <eaglesondouglas(a)yahoo.com> wrote: >On Mar 13, 1:52 pm, 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 are rather importent things to try to get correct. I am still >looking for some references, easy web kind, to allow topology to >express points. > >And if a point was expressable, a function. And so nth topoogy is >possible, but I need a Matlab transform that links a theorm, to the >applied coordinate. And so the basic idea is to allow points where the >size as infinity are expressable. > >This solves a symmetry problem. And resolves the question of sets of >rationals to irrationals as true sized, infinities! > >So the topology of the point is a theorm I need. > >Any ideas? Well if the intersection of lines defines points it indeed occurs to me that points must be spherical since lines can double back on themselves from all different directions. However that suggests as well that if the contention of mathematkers is true then points constituting a line must connect through points on each sphere. ~v~~
From: �u�Mu�PaProlij on 13 Mar 2007 18:18 > Bucky Fuller's kindergarten teacher gave her class semi-dried peas and > toothpicks to build "structures". All of the kids built structures that > had 90 degree angles like squares and cubes except Bucky. He could not > see because he didn't have a pair of glasses yet, and felt that the > triangle and tetrahedron were strong, but the square and cube did not > hold their shape. He got a patent for the structure he made about 60 > years later. He thought like a child for about 60 years and started to > write Synergetics. 15 years later the first volume was published. > it is nice story but nothing more. It is one of the stories that fits in "how to become rich and successful" book, chapter "Change the way you think and all your problems will be solved"
From: Lester Zick on 13 Mar 2007 18:20 On 13 Mar 2007 13:30:17 -0700, "Douglas Eagleson" <eaglesondouglas(a)yahoo.com> wrote: >On Mar 13, 3:08 pm, "Douglas Eagleson" <eaglesondoug...(a)yahoo.com> >wrote: >> On Mar 13, 1:52 pm, 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 are rather importent things to try to get correct. I am still >> looking for some references, easy web kind, to allow topology to >> express points. >> >> And if a point was expressable, a function. And so nth topoogy is >> possible, but I need a Matlab transform that links a theorm, to the >> applied coordinate. And so the basic idea is to allow points where the >> size as infinity are expressable. >> >> This solves a symmetry problem. And resolves the question of sets of >> rationals to irrationals as true sized, infinities! >> >> So the topology of the point is a theorm I need. >> >> Any ideas? >> >> Thanks Doug > >If you think points are trivial in topology please give me your >reference. Because the Dekind Cut as the rate expresses the infinite >sequence of all. A size as absolute infinite expression was his >abstract size! > >Always was it a small little cut of exact size. > >So the appearance of the?????? > >And here we sit. > >A bunch of question marks. Abstract the Cut, no big deal? > >It is hard for me to accept Dekind's invention in the first place >until you are informed you need assitance. SO it is hard stuff. What >is a Dekind cut? > >And if you can answer, then the relation of its cause in geometric >space is apparent. SO a single little theorm I am ignorent of. >Please help. I don't see points as having any topology. That's what makes them points. Nor do I see points as making up lines. That's egregiously absurd on the face of it. And it is scarcely supportable just because mathematikers make up a pointless circular line of reasoning. ~v~~
From: Lester Zick on 13 Mar 2007 18:28
On Tue, 13 Mar 2007 20:48:34 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: >> 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 . . . >> > >point is coordinate in (any) space (real or imaginary). >For example (x,y,z) is a point where x,y and z are any numbers. That's nice. And I'm sure we could give any number of other examples of points. Very enlightening indeed. However the question at hand is whether points constitute lines and whether or not circular lines of reasoning support that contention. >line is collection of points and is defined with three functions >x = f(t) >y = g(t) >z = h(t) > >where t is any real number and f,g and h are any continous functions. > >Your definition is good for 10 years old boy to understand what is point and >what is line. (When I was a child, I thought like a child, I reasoned like a >child. When I became a man, I put away childish ways behind me.....) Problem is you may have put away childish things such as lines and points but you're still thinking like a child. Are points and lines not still mathematical objects and are lines made up of points just because you got to be eleven? ~v~~ |