The Definition of Points
in [Math]
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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~~
From: Lester Zick on 14 Mar 2007 19:25
On Wed, 14 Mar 2007 11:45:59 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Eckard Blumschein wrote:> 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. > >Points don't glide. In fact points don't move. You are still pushing >discrete mathematics? All you will get is a means of totalling up your >grocery bill. Arithmetic forever. Points glide at least as much as you do, Bob. ~v~~ |