The Definition of Points
in [Math]
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From: SucMucPaProlij on 17 Mar 2007 12:51 >> So, essentially, anything that's not self-contradictory exists, or is >> "true"? In an infinite universe, perhaps.... > > 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. > Wrong! If idea doesn't have any material form and it is not even energy, magnetic field of enything else, then you have Altzhaimer and idea is lost :)))))
From: SucMucPaProlij on 17 Mar 2007 12:54 > > 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!
From: alanmc95210 on 17 Mar 2007 13:00 On Mar 16, 10:48 am, "ken.quir...(a)excite.com" <ken.quir...(a)excite.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~~ > > My impression is that Euclid defined a line, not in terms of points, > and never claimed a line was made up of points, but defined a line as > a geometrical object that has only the property of extensibility > (length, > where length can be infinite). > > He uses points in his proofs specifically as intersections of lines, > if I > remember correctly, and makes no attempt at describing or > explaining their density in a line. (You gotta lot of 'splainin to do, > Euclid!). Euclid established the foundation for our mathematical deduction system. As he realized from his Axioms and Postulates, you can't prove everything. You've got to start with some given Axioms. Lines and points are among those basic assumptions- A. McIntire
From: nonsense on 17 Mar 2007 13:00 SucMucPaProlij wrote: > Can you define a difference between intuitive point and real apple? > How matematikers handle reality? Sometimes even a troll asks a good question. A point and an apple are self defining. We only get to report about them. Please refer to Clinton's comment about the meaning of "is".
From: nonsense on 17 Mar 2007 13:01
SucMucPaProlij wrote: >>>So, essentially, anything that's not self-contradictory exists, or is >>>"true"? In an infinite universe, perhaps.... >> >>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. >> > > > Wrong! > If idea doesn't have any material form and it is not even energy, magnetic field > of enything else, then you have Altzhaimer and idea is lost :))))) You're missing the point. A concept is a report, not the reality. Blind men and the elephant and all. |