The Definition of Points
in [Math]
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From: Lester Zick on 13 Mar 2007 13:52 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~~
From: Ross A. Finlayson on 13 Mar 2007 14:20 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~~ You should ask me. Ross -- Finlayson Consulting
From: PD on 13 Mar 2007 14:34 On Mar 13, 12:52 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~~ Interestingly, the dictionary of the English language is also circular, where the definitions of each and every single word in the dictionary is composed of other words also defined in the dictionary. Thus, it is possible to find a circular route from any word defined in the dictionary, through words in the definition, back to the original word to be defined. That being said, perhaps it is in your best interest to find a way to write a dictionary that eradicates this circularity. That way, when you use the words "peculiar" and "definitional", we will have a priori definitions of those terms that are noncircular, and from which the unambiguous meaning of what you write can be obtained. PD
From: Sam Wormley on 13 Mar 2007 14:43 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."
From: Douglas Eagleson on 13 Mar 2007 15:08
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 |