The Definition of Points
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From: Lester Zick on 14 Mar 2007 14:44 On Wed, 14 Mar 2007 10:05:05 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: >> >> You don't have to accept anything. It might be nice however if you had >> some tenable alternative to suggest. Are you suggesting lines are not >> made up of points and the intersection of lines does not define a >> point? Or are you suggesting we just ignore the problem because modern >> mathematikers are too lazy or stupid to resolve it? >> > >I think that you are just playing dumb. I can speak as well as anyone and better than most. >"Line is made of points" is not definition of line and modern mathematikers can >resolve your questions. Oookay. >Intersection of lines can define a point and we both know it Can define a point or does define a point? And if the former what exactly defines a point without the intersection of lines? > just as we both >know that line is made of points. Either this comment is facetious or you like to hold all opinions at once. >If you don't think that line is made of points then how do you explain the fact >that two lines can have common point? Rather easily if their intersection defines the point. But I don't see that this has any bearing on whether lines are made up of points. Intersections of lines defining points would still be made up of the points making up the lines. The reasoning is still circular. > If two lines are intersecting in a point >is this point one part of both lines or is it created during intersectioning? If the point is defined by the intersection what happens to the point and what defines the point when the lines don't interesect? On the other hand if the point is not defined by the intersection of lines how can one assume the line is made up of things which aren't defined? ~v~~
From: The_Man on 14 Mar 2007 14:59 On Mar 14, 12:50 am, Lester Zick <dontbot...(a)nowhere.net> wrote: > On Tue, 13 Mar 2007 23:40:39 +0100, "SucMucPaProlij" > > > > > > <mrjohnpauldike2...(a)hotmail.com> wrote: > > >"Lester Zick" <dontbot...(a)nowhere.net> wrote in message > >news:2t8ev292sqinpej146h9b4t4o4n9pvr8c2(a)4ax.com... > >> On Tue, 13 Mar 2007 20:48:34 +0100, "SucMucPaProlij" > >> <mrjohnpauldike2...(a)hotmail.com> wrote: > > >>>> 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 . . . > > >>>point is coordinate in (any) space (real or imaginary). > >>>For example (x,y,z) is a point where x,y and z are any numbers. > > >> That's nice. And I'm sure we could give any number of other examples > >> of points. Very enlightening indeed. However the question at hand is > >> whether points constitute lines and whether or not circular lines of > >> reasoning support that contention. O.K. Tell us, Icky-po: What do YOU think lines are made of? What do YOU think is a "suitable" definition for point, line, plane, etc.. I'm sure Gauss, Euler, Cantor, Cauchy, Riemann, and Hilbert are rolling over in their graves with anticipation. Maybe the crew of my local Burger King will redefine QM next week, and the Friendly's will unify all the forces of nature in one theory. > > >>>line is collection of points and is defined with three functions > >>>x = f(t) > >>>y = g(t) > >>>z = h(t) > > >>>where t is any real number and f,g and h are any continous functions. > > >>>Your definition is good for 10 years old boy to understand what is point and > >>>what is line. (When I was a child, I thought like a child, I reasoned like a > >>>child. When I became a man, I put away childish ways behind me.....) > > >> Problem is you may have put away childish things such as lines and > >> points but you're still thinking like a child. > > >> Are points and lines not still mathematical objects and are lines made > >> up of points just because you got to be eleven? > > >> ~v~~ > > >hahahahaha > >the simple answer is that line is not made of anything. Line is just > >abstraction. Properties of line comes from it's definition. > > Which is all just swell. So now the question I posed becomes are > abstract lines made up of abstract points? > > >Is line made of points? > >If you don't define term "made of" and use it without too much thinking you can > >say that: > > Why don't you ask Bob Kolker. He seems to think lines are "made up" of > points, abstract or otherwise. I'm not quite clear about how he thinks > lines are "made up" of points but he nonetheless seems to think they > are. > > >line is defined with 3 functions: > >x = f(t) > >y = g(t) > >z = h(t) > > >where (x,y,z) is a point. As you change 't' you get different points and you say > >that line is "made of" points, but it is just an expressions that you must fist > >understand well before you question it. > > Frankly I prefer to question things before I waste time learning them. Yes -learning things is such a "waste". That's why you know so little. > > ~v~~- Hide quoted text - > > - Show quoted text -
From: Lester Zick on 14 Mar 2007 15:03 On Wed, 14 Mar 2007 09:07:14 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >SucMucPaProlij wrote: > >> >> Intersection of lines can define a point and we both know it just as we both >> know that line is made of points. >> >> If you don't think that line is made of points then how do you explain the fact >> that two lines can have common point? If two lines are intersecting in a point >> is this point one part of both lines or is it created during intersectioning? > >Maybe he thinks there are objects other than points on lines. If so, >they are not ever mentioned in any axiom system for Euclidean Geometry. Objects other than points on lines, Bob? Show me the points on lines without intersection with other lines. You're a little confused.Points aren't on lines. They're at or on the intersection of lines. >Likwise for planar curves. L.Z. rejects the usual definition of a cirlce >as a set of points on a plane a given distance (the radius) from a >specified point (the center). The hell you say, Bob. What LZ rejects is the conventional practice of mathematikers in co opting geometric objects while pretending they're doing SOAP arithmetic definitions without geometry. > If a circle does not consist of its >points, what else besides points lie on the circle? Your logic? > If there are any >such objects they are never mentioned in the axioms. Begging the question is often employed by but rarely mentioned in axioms. >Zick'w problem (among several problems he has) is that he simply does >not comprehend what an axiomatic system is. Of course I do. It's a series of undemonstrable empirical assumptions whose truth can only be guessed at and whose falsity is concealed with implausible definitions which are defined as neither true nor false. > He cannot comprehend the >notion of undefined terms or objects whose only properties are given in >the axioms. Sure I can. Except when axiomatic assumptions prove false or definitions prove untrue. Minor problem I admit but there it is. > For example, whatever a point is, given two distinct points >there is one and only one line (whatever a line is) containing them. Well more likely the two distinct points define a straight line segment which doesn't actually contain the points since the points define the straight line segment and not vice versa. In other words distinct points contain the straight line segment. See, Bob, this is the whole problem with SOAP definitions. Between every pair of "distinct" points a straight line segment is defined and not a curve. That's what makes the points distinct to begin with. In point of fact I'd like to see you show us some "indistinct" points and tell us exactly what they define. ~v~~
From: Lester Zick on 14 Mar 2007 15:06 On Wed, 14 Mar 2007 14:23:34 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: > >"Bob Kolker" <nowhere(a)nowhere.com> wrote in message >news:55qac4F24r2boU1(a)mid.individual.net... >> SucMucPaProlij wrote: >> >>> >>> Intersection of lines can define a point and we both know it just as we both >>> know that line is made of points. >>> >>> If you don't think that line is made of points then how do you explain the >>> fact that two lines can have common point? If two lines are intersecting in a >>> point is this point one part of both lines or is it created during >>> intersectioning? >> >> Maybe he thinks there are objects other than points on lines. If so, they are >> not ever mentioned in any axiom system for Euclidean Geometry. >> > >One can assume that there are some objects other than points but I don't think >that anyone can prove that this objects are not points becouse you can't tell a >difference between single point that stands alone and some imaginary object that >is on a line. They both have the same simple characteristics (coordinates) and >that is all they have. The difficulty isn't whether there are objects on lines but whether lines are composed of them. Certainly points are properties of the intersection of lines and are not defined on lines in themselves. >> Likwise for planar curves. L.Z. rejects the usual definition of a cirlce as a >> set of points on a plane a given distance (the radius) from a specified point >> (the center). If a circle does not consist of its points, what else besides >> points lie on the circle? If there are any such objects they are never >> mentioned in the axioms. >> >> Zick'w problem (among several problems he has) is that he simply does not >> comprehend what an axiomatic system is. He cannot comprehend the notion of >> undefined terms or objects whose only properties are given in the axioms. For >> example, whatever a point is, given two distinct points there is one and only >> one line (whatever a line is) containing them. >> > >well, nobody is perfect... What never? Well . . . hardly ever. ~v~~
From: Lester Zick on 14 Mar 2007 15:12
On Wed, 14 Mar 2007 10:07:49 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >SucMucPaProlij wrote:> >> >> One can assume that there are some objects other than points but I don't think > >Only if one makes this assumption explicit. This means introducing >objects other than points and lines into the system and it means some >axiom must somehow mention and characterize this additional object or >kind of object. Well for that matter why introduce points into the system except as the intersection of lines? The obvious answer is so that mathematikers can pretend they're doing arithmetic with SOAP definitions instead of geometry. >The idea of an axiom system such as Hilbert's is to -explicitly- mention >those objects which are not defined and characterize them with the >axioms. Thus, given two distinct points there is one and only one line >containing the points. The containment relation expressed in a number of >ways is also undefined. We we say a point is on a line. A line contains >a point or a line passes through a point etc.. In other words you can just make the problem go away with erroneous definitions? Straight line segments don't contain points; points contain straight line segments. Hell points don't even contain curves. ~v~~ |