The Definition of Points
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From: SucMucPaProlij on 17 Mar 2007 13:10 <nonsense(a)unsettled.com> wrote in message news:56b33$45fc1e98$4fe72e0$21877(a)DIALUPUSA.NET... > 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. I don't understand. You didn't ask any question. > > A point and an apple are self defining. We only > get to report about them. > good. How do you explain that point exists in math but doesn't exist in real word? Why is that? > Please refer to Clinton's comment about the meaning > of "is". > > >
From: SucMucPaProlij on 17 Mar 2007 13:24 <nonsense(a)unsettled.com> wrote in message news:b71c5$45fc1f22$4fe72e0$21877(a)DIALUPUSA.NET... > 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 can't define points and lines with numbers and sets? Try it. It is not hard.
From: Bob Kolker on 17 Mar 2007 13:47 SucMucPaProlij wrote: > > > Can you define a difference between intuitive point and real apple? > How matematikers handle reality? You can make apple sauce from an apple. You can't make point fritters. Bob Kolker > >
From: Bob Kolker on 17 Mar 2007 13:49 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! Not true. One of the mathematical systems which satisfy Hilbert's Axioms for plane geometry is RxR , where R is the real number set. Points are ordered pairs of real numbers. Not a scintilla of geometry there. Bob Kolker > >
From: Bob Kolker on 17 Mar 2007 13:50
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. Bob Kolker > |