The Definition of Points
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From: SucMucPaProlij on 14 Mar 2007 17:30 > If the point is defined by the intersection what happens to the point > and what defines the point when the lines don't intersect? > 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? > hahahahaha you are poor philosopher. Math can't create the world it can only (try to) explain it. To explain something you must fist admit that something exists. I admit that lines and points do exist. Every definition puts in relation two or more thing that exist. Definition of point doesn't create point. It puts point in relation to something else. If you define point with intersection of two lines you put in relation: 1) point that you admit that already exists 2) two lines that you admit that already exist 3) and their intersection that you admit that already exists. Definition also does not create relation between thing. Relation between point, two lines and their intersection already exists and with definition you only admit that it exists. When you say "point is intersection of two lines" then you only admit that there exist certain relation between point, two lines and their intersection. This relation will also exist if you don't define it because definition discovers relations, it does not create them. Who (beside you) claims that it is wrong to define point with lines and define line with points? Definition of point says that there is some relation R1 between point P and lines L1 and L2 R1 = {(R, L1, L2) | where blabla P bla L1 and blabla L2} "Line is made up of points" says that there is relation R2 between line L and point P R2={(L,P) | where blabla L and blabla P} Not all relations are in form y=f(x) nor they should be. It is true that you can define point without intersection of two lines and it is true that you can define line without points but it only means that there is certain relation between point and something that is not line, and there is certain relation between lines and something that is not point. It is also true that you can't define point using nothing nor you can define line using nothing because relation between point and nothing is just not relation and therefore definition that defines something using nothing is just not definition. Just as f(x)=x-2*f(x) if perfectly good definition of f(x), "point is intersection of lines and line is made out of points" is ok definition if you know how to use it. Someone is confused with f(x)=x-2*f(x) and someone else is confused with points and lines :)))))
From: Eric Gisse on 14 Mar 2007 17:54 On Mar 14, 11:15 am, Lester Zick <dontbot...(a)nowhere.net> wrote: > On 13 Mar 2007 23:21:54 -0700, "Eric Gisse" <jowr...(a)gmail.com> wrote: > > > > >On Mar 13, 9:54 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > >> On 13 Mar 2007 17:18:03 -0700, "Eric Gisse" <jowr...(a)gmail.com> wrote: > > >> >On Mar 13, 9:52 am, Lester Zick <dontbot...(a)nowhere.net> wrote: > >> >> The Definition of Points > >> >> ~v~~ > > >> >> 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 . . . > > >> >> ~v~~ > > >> >Points, lines, etc aren't defined. Only their relations to eachother. > > >> So is the relation between points and lines is that lines are made up > >> of points and is the relation between lines and points that the > >> intersection of lines defines a point? > > >No, it is more complicated than that. > > Well that's certainly a relief. I thought you said "only their > relations to each other". It's certainly good to know that what lines > are made up of is not "only a relation" between points and lines. > > ~v~~ No, I said "it is more complicated than that." http://en.wikipedia.org/wiki/Hilbert's_axioms
From: exp(j*pi/2) on 14 Mar 2007 19:12 On Mar 14, 12:24 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > On Tue, 13 Mar 2007 23:28:19 -0700, Bob Cain > > <arc...(a)arcanemethods.com> wrote: > >The_Man wrote: > > >> What do YOU produce, Mister Nick Ick? What have YOU accomplished? > > >He's good at starting vanity threads to demonstrate his self > >proclaimed and self appreciated wit. > > Better to be witty than witless I suppose. > > >He's a legend in his own mind. > > And in the minds of others too, Stringfellow. You seem to think these > threads are one sided extemporaneous lectures on my part. You also > seemed to think Ken Seto and I would have some kind of monumental > donnybrook. You also pretty much just seem to think when you don't. > > ~v~~ Actually, Bob Cain's fundamental problem is that when he looks into a mirror he sees everyone except himself.
From: Lester Zick on 14 Mar 2007 19:22 On Wed, 14 Mar 2007 15:51:34 +0100, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > >On 3/13/2007 6:52 PM, Lester Zick wrote: >> >> In the swansong of modern math lines are composed of points. But then >> we must ask how points are defined? > >I hate arbitrary definitions. I would rather like to pinpoint what makes >the notion of a point different from the notion of a number: Well I'm not exactly sure what a number is supposed to be. I know modern mathematikers claim numbers are supposed to be this and that. However no one seems to understand what this and that is supposed to mean. >If a line is really continuous, then a mobile point can continuously >glide on it. If the line just consists of points corresponding to >rational numbers, then one can only jump from one discrete position to >an other. Just like modern mathematikers can jump from one position to another. >A point has no parts, each part of continuum has parts, therefore >continuum cannot be resolved into any finite amount of points. >Real numbers must be understood like fictions. Or perhaps like functions. >All this seems to be well-known. When will the battle between frogs and >mices end with a return to Salviati? Perhaps when modern mathematikers concern themselves with truth instead of fiction? ~v~~
From: Lester Zick on 14 Mar 2007 19:24
On 14 Mar 2007 08:07:33 -0700, "PD" <TheDraperFamily(a)gmail.com> wrote: >On Mar 14, 9:51 am, Eckard Blumschein <blumsch...(a)et.uni-magdeburg.de> >wrote: >> On 3/13/2007 6:52 PM, Lester Zick wrote: >> >> >> >> > In the swansong of modern math lines are composed of points. But then >> > we must ask how points are defined? >> >> I hate arbitrary definitions. I would rather like to pinpoint what makes >> the notion of a point different from the notion of a number: >> >> If a line is really continuous, then a mobile point can continuously >> glide on it. If the line just consists of points corresponding to >> rational numbers, then one can only jump from one discrete position to >> an other. > >That's an interesting (but old) problem. How would one distinguish >between continuous and discrete? As a proposal, I would suggest means >that there is a finite, nonzero interval (where interval is measurable >somehow) between successive positions, in which there is no >intervening position. Unfortunately, the rational numbers do not >satisfy this definition of discreteness, because between *any* two >rational numbers, there is an intervening rational number. I'd be >interested in your definition of discreteness that the rational >numbers satisfy. That there is a straight line segment between rational numbers? >> A point has no parts, each part of continuum has parts, therefore >> continuum cannot be resolved into any finite amount of points. >> Real numbers must be understood like fictions. >> >> All this seems to be well-known. When will the battle between frogs and >> mices end with a return to Salviati? > ~v~~ |