The Definition of Points
in [Math]
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From: Lester Zick on 16 Mar 2007 19:48 On Fri, 16 Mar 2007 04:05:59 GMT, Sam Wormley <swormley1(a)mchsi.com> wrote: >Lester Zick wrote: >> On Thu, 15 Mar 2007 13:21:19 GMT, Sam Wormley <swormley1(a)mchsi.com> >> wrote: >> >>> Bob Kolker wrote: >>>> Sam Wormley wrote: >>>> >>>>> Hey Lester-- >>>>> >>>>> 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." >>>> That really is not a definition in the species-genus sense. It is a >>>> -notion- expressing an intuition. At no point is that "definition" ever >>>> used in a proof. Check it out. >>>> >>>> Many of Euclid's "definitions" were not proper definitions. Some where. >>>> The only things that count are the list of undefined terms, definitions >>>> grounded on the undefined terms and the axioms/postulates that endow the >>>> undefined terms with properties that can be used in proofs. >>>> >>>> Bob Kolker >>> Give me something better, Bob, or are you arguing there isn't a better >>> definition (if you can call it that). >> >> Well we can always pretend there is something better but that doesn't >> necessarily make it so. I think modern mathematikers have done such a >> first rate job at the pretense that it's become a doctrinal catechism. >> >> ~v~~ > > > What's your formal education in mathemaitcs, Lester? U.S. Naval Academy, Annapolis, MD. 1966 BSME. I'm sure they can provide cv's to such worthy souls.Finished playing trivial pursuit now and may we return to discussing the problem at hand or would you prefer further essays on educational effluvia? ~v~~
From: Lester Zick on 16 Mar 2007 19:51 On Fri, 16 Mar 2007 04:04:50 GMT, Sam Wormley <swormley1(a)mchsi.com> wrote: >Lester Zick wrote: >> On Thu, 15 Mar 2007 13:59:08 GMT, Sam Wormley <swormley1(a)mchsi.com> >> wrote: >> >>> Bob Kolker wrote: >>>> Sam Wormley wrote: >>>> >>>>> Give me something better, Bob, or are you arguing there isn't a better >>>>> definition (if you can call it that). >>>> You are asking for a definition of an undefined term. There is nothing >>>> better. If one finds a definition of point it will have to be based on >>>> something undefined (eventually) otherwise there is circularity or >>>> infinite regress. We can't have mathematics based on turtles all the way >>>> down. There has to be starting point. >>>> >>>> Here is my position. If an alleged definition is no where used in proofs >>>> it should be eliminated or clear marked as an intuitive insight. >>>> >>>> Bob Kolker >>>> >>> Fair enough--However, for conceptualizing "defining" a point >>> with coordinate systems suffices. >> >> However it does not suffice for the definition of lines and arguments, >> proofs, and justifications based on such assumptions. Defining points >> is hardly essential to definition of lines based on such definitions. >> >> ~v~~ > > Hey Lester > Line > http://mathworld.wolfram.com/Line.html > > "A line is uniquely determined by two points, and the line passing > through points A and B". > > "A line is a straight one-dimensional figure having no thickness and > extending infinitely in both directions. A line is sometimes called > a straight line or, more archaically, a right line (Casey 1893), to > emphasize that it has no "wiggles" anywhere along its length. While > lines are intrinsically one-dimensional objects, they may be embedded > in higher dimensional spaces". Hey, Sam - http://www.webeenoverthisshitalreadysoifyouhavenothingfurther? ~v~~
From: Lester Zick on 16 Mar 2007 19:53 On 16 Mar 2007 07:26:57 -0700, "hagman" <google(a)von-eitzen.de> wrote: >On 15 Mrz., 23:54, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On Thu, 15 Mar 2007 11:38:50 -0400, Bob Kolker <nowh...(a)nowhere.com> >> wrote: >> >> >Sam Wormley wrote: >> >The fact that RxR with a metric satisfies the Hilbert Axioms for plane >> >geometry implies that points can be taken to be pairs of real numbers. >> >> As a guess not bad. As a mathematical assumption pretty awful. > >There's no assumption in here. >"RxR satisfies Hilbert axioms for plane geometry" is provable. >"Foo satisfies the axioms of a Bar object" means that all theroems of >Bar theory are true when interpreted as statements about Foo. Okay, hag. My observation was in regards to those axioms not whether they're satisfied by a bunch of self righteous empirical observations. ~v~~
From: Lester Zick on 16 Mar 2007 19:53 On Thu, 15 Mar 2007 20:01:32 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Eric Gisse wrote: > >> On Mar 15, 2:54 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> [...] >> >> What is your background in mathematics, Lester? > >You have asked: "what is the empty set". And "Bob" is the answer. ~v~~
From: Lester Zick on 16 Mar 2007 19:54
On 15 Mar 2007 16:01:25 -0700, "Eric Gisse" <jowr.pi(a)gmail.com> wrote: >On Mar 15, 2:54 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > >[...] > >What is your background in mathematics, Lester? 1, 2, 3, that's all we happen to be . . . ~v~~ |