The Definition of Points
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From: Bob Kolker on 17 Mar 2007 13:52 nonsense(a)unsettled.com wrote: > > Sometimes even a troll asks a good question. > > A point and an apple are self defining. We only > get to report about them. Apples are defined by ostention. One points to an apple and says "apple". That is how babies learn what basic words mean. Many of the basic worlds we use are defined by pointing to objects and attaching the word to the object. Logical definitions occur at a higher level of abstraction. Bob Kolker
From: Bob Kolker on 17 Mar 2007 13:54 SucMucPaProlij wrote: > > > You can't define points and lines with numbers and sets? > Try it. It is not hard. Points (in n-dimesnsional space) are ordered n-tuples of real numbers. Bob Kolker
From: Hero on 17 Mar 2007 14:09 Bob Kolker wrote: > SucMucPaProlij wrote: > > > And I agree but can you tell me does point exist? > > How do you explain it? > > Point is an idea or a notion. It has no physical existence. Neither does > the integer 1. > > Point is a place holder for an intuition about space. Nothing more. > Along with line, plane and a few other place holders they constitute the > undefined terms of geometry. Intuitive notions are useful guides for > finding logical proofs, but they have not probatory or logical standing. > Referring to .." they have not probatory...standing". This associates: If You want to put down a glass onto a table and You are holding it's base a bit skew it might get a standing, but being pushed by someone at this moment it might tumble - and this has to do with it's point of gravity. With friendly greetings Hero PS. I just wonder, if a point relates to the word "pointing"?
From: Hero on 17 Mar 2007 14:23 On 17 Mrz., 18:49, Bob Kolker <nowh...(a)nowhere.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! > > 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. > Left and right are geometrical concepts. When You write down ( 3, 4 ) 3 is left in Your view and 4 is right. With friendly greetings Hero
From: VK on 17 Mar 2007 14:29
On Mar 16, 2:26 am, Lester Zick <dontbot...(a)nowhere.net> wrote: > >> I believe Lester is asking whether a line is a composite object or an > >> atomic primitive. > > >That is one of things and the most easy one. I believe I already gave > >the answer but not sure that he will ever accept it > > Oh I accept it all right. I just don't understand it. So you don't understand that a abstraction - having no exact equivalence in the perceived world - may be defined in different ways? Let me ask a question then if you don't mind. Given a few definition of the abstraction in question: 1) a point is what doesn't have sides 2) a point is n intersection of two lines 3) a point is to ti en einai of infinity .... n) a point is a reversed infinity where between 3 and n feel free to place whatever is missing in any amount. So given this set of definitions: would you agree that only one definition is possibly true among all given ones? Would you agree that for any abstraction among all possible definitions there is one and only one which is correct? So the task is not to define an abstraction in a custom and possibly erroneous way - but the task it to find that pre-existing true definition among all possible ones? Three questions in total but really only one as promised, just making myself as clear as possible. It is also not a rhetoric question with a "proper" answer implied, I'm really asking you: yes or no? |