The Definition of Points
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From: Lester Zick on 17 Mar 2007 19:30 On Sat, 17 Mar 2007 09:40:03 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >SucMucPaProlij wrote: > >> >> Mathematikers do claim that math has nothing to do with reality but if it is >> true you can't use math to prove it because math has nothing to do with reality. >> It means that there is little possibility that math has some connections with >> real world. > >Mathematics has an instrumental connection with the world. It makes >physics possible. Isaac Newton first had to invent calculus to develop a >physical theory of dynamic motion. > >Without mathematics there is no physics. True but without SOAP operas we'd still have mathematics. ~v~~
From: Lester Zick on 17 Mar 2007 19:33 On Sat, 17 Mar 2007 13:50:01 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >alanmc95210(a)yahoo.com wrote:> >> 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 > >The lines and points are undefined objects. It is the axioms concerning >lines and points that are the basic assumptions. "Assumptions" being the operative word. It might be nice if we could get a little closer to "truth" for a change. ~v~~
From: Lester Zick on 17 Mar 2007 19:34 On Sat, 17 Mar 2007 12:03:44 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Tony Orlow wrote: > >> Yes, the relationship between points and lines is rather codependent, >> isn't it? I looked at some of the responses, and indeed, one can define >> points as tuples of coordinates, but of course, that all depends on >> defining a set of dimensions as a space to begin with, each dimension >> constituting an infinite line along which that coordinate is defined. In >> language, both points and lines are taken as primitives, since their >> properties are not rooted in symbols and strings, but geometry. So, we >> may be left with the question as to what the primitives of geometry >> really are, sets of points, or sequences of lines. That's the conundrum >> right, that differences and differences between differences are lines, >> and not points? :) > >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. So you can develop geometry without assuming any geometrical notions? I don't see any evidence modern math has managed to any thing of the kind. ~v~~
From: Lester Zick on 17 Mar 2007 19:36 On Sat, 17 Mar 2007 17:54:17 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: >> >> 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! Yeah, Bob, please define circles, planes, etc. in terms of SOAP operas without reference to geometrical notions. ~v~~
From: Lester Zick on 17 Mar 2007 19:39
On Sat, 17 Mar 2007 11:02:30 -0600, "nonsense(a)unsettled.com" <nonsense(a)unsettled.com> wrote: >SucMucPaProlij wrote: > >>>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! > >No they're not. "The locus of all points...." You mean kinda like "a circle is the locus of all points on a plane equidistant from any point", Bob? Good to know we don't need geometry anymore. I think the more pertinent question is why we need you? ~v~~ |