The Definition of Points
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From: Lester Zick on 21 Mar 2007 15:20 On Wed, 21 Mar 2007 07:40:46 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Tony Orlow wrote: >> >> There is no correlation between length and number of points, because >> there is no workable infinite or infinitesimal units. Allow oo points >> per unit length, oo^2 per square unit area, etc, in line with the >> calculus. Nuthin' big. Jes' give points a size. :) > >Points (taken individually or in countable bunches) have measure zero. They probably also have zero measure in uncountable bunches, Bob. At least I never heard that division by zero was defined mathematically even in modern math per say. ~v~~
From: Mike Kelly on 21 Mar 2007 15:32 On 21 Mar, 19:17, Lester Zick <dontbot...(a)nowhere.net> wrote: > On 21 Mar 2007 02:15:20 -0700, "Mike Kelly" > > > > <mikekell...(a)googlemail.com> wrote: > >On 21 Mar, 05:47, Tony Orlow <t...(a)lightlink.com> wrote: > >> step...(a)nomail.com wrote: > >> > In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >> >> PD wrote: > >> >>> No one says a set of points IS in fact the constitution of physical > >> >>> object. > >> >>> Whether it is rightly the constitution of a mentally formed object > >> >>> (such as a geometric object), that seems to be an issue of arbitration > >> >>> and convention, not of truth. Is the concept of "blue" a correct one? > > >> >>> PD > > >> >> The truth of the "convention" of considering higher geometric objects to > >> >> be "sets" of points is ascertained by the conclusions one can draw from > >> >> that consideration, which are rather limited. > > >> > How is it limited Tony? Consider points in a plane, where each > >> > point is identified by a pair of real numbers. The set of > >> > points { (x,y) | (x-3)^2+(y+4)^2=10 } describes a geometric object. > > >> That's a very nice circle, Stephen, very nice.... > > >> > In what way is this description "limited"? Can you provide a > >> > better description, and explain how it overcomes those limitations? > > >> There is no correlation between length and number of points > > >Oh. And I suppose there *is* such a correlation in "real" geometry? > > There is if you approach the definition of points on a line through > real geometric subdivision instead of trying to glom line segments > together into a straight line ala Frankenstein's monster per say. > > ~v~~ Don't waste time responding to me. I have no interest in conversing with trolls, no matter how clever or amusing they think themselves. -- mike.
From: Mike Kelly on 21 Mar 2007 15:35 On 21 Mar, 19:17, Tony Orlow <t...(a)lightlink.com> wrote: > Mike Kelly wrote: > > On 21 Mar, 15:47, Tony Orlow <t...(a)lightlink.com> wrote: > >> Mike Kelly wrote: > >>> On 21 Mar, 05:47, Tony Orlow <t...(a)lightlink.com> wrote: > >>>> step...(a)nomail.com wrote: > >>>>> In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >>>>>> PD wrote: > >>>>>>> No one says a set of points IS in fact the constitution of physical > >>>>>>> object. > >>>>>>> Whether it is rightly the constitution of a mentally formed object > >>>>>>> (such as a geometric object), that seems to be an issue of arbitration > >>>>>>> and convention, not of truth. Is the concept of "blue" a correct one? > >>>>>>> PD > >>>>>> The truth of the "convention" of considering higher geometric objects to > >>>>>> be "sets" of points is ascertained by the conclusions one can draw from > >>>>>> that consideration, which are rather limited. > >>>>> How is it limited Tony? Consider points in a plane, where each > >>>>> point is identified by a pair of real numbers. The set of > >>>>> points { (x,y) | (x-3)^2+(y+4)^2=10 } describes a geometric object. > >>>> That's a very nice circle, Stephen, very nice.... > >>>>> In what way is this description "limited"? Can you provide a > >>>>> better description, and explain how it overcomes those limitations? > >>>> There is no correlation between length and number of points > >>> Oh. And I suppose there *is* such a correlation in "real" geometry? > >>> -- > >>> mike. > >> In my geometry |{x in R: 0<x<=1}| = Big'Un (or oo). > > > What does that have to do with geometry? > > > -- > > mike. > > It states the specific infinite number of points in the unit interval, > say, on the real line. And I ask again, what does that have to do with geometry? Stephen already pointed out that saying "there are BigUn points in a unit interval" doesn't tell us anything interesting about anything. It doesn't add any information. It doesn't lead to any new theorems of any consequence. So why bother? -- mike.
From: Mike Kelly on 21 Mar 2007 15:37 On 21 Mar, 19:20, Tony Orlow <t...(a)lightlink.com> wrote: > step...(a)nomail.com wrote: > > In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >> step...(a)nomail.com wrote: > >>> In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >>>> step...(a)nomail.com wrote: > >>>>> In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >>>>>> PD wrote: > >>>>>>> No one says a set of points IS in fact the constitution of physical > >>>>>>> object. > >>>>>>> Whether it is rightly the constitution of a mentally formed object > >>>>>>> (such as a geometric object), that seems to be an issue of arbitration > >>>>>>> and convention, not of truth. Is the concept of "blue" a correct one? > > >>>>>>> PD > > >>>>>> The truth of the "convention" of considering higher geometric objects to > >>>>>> be "sets" of points is ascertained by the conclusions one can draw from > >>>>>> that consideration, which are rather limited. > >>>>> How is it limited Tony? Consider points in a plane, where each > >>>>> point is identified by a pair of real numbers. The set of > >>>>> points { (x,y) | (x-3)^2+(y+4)^2=10 } describes a geometric object. > >>>> That's a very nice circle, Stephen, very nice.... > >>> Yes, it is a circle. You knew exactly what this supposedly > >>> "limited" description was supposed to be. > > >>>>> In what way is this description "limited"? Can you provide a > >>>>> better description, and explain how it overcomes those limitations? > >>>> There is no correlation between length and number of points, because > >>>> there is no workable infinite or infinitesimal units. Allow oo points > >>>> per unit length, oo^2 per square unit area, etc, in line with the > >>>> calculus. Nuthin' big. Jes' give points a size. :) > >>> How is that a limitation? You knew exactly what shape the > >>> set of points described. There is no feature of the circle > >>> that cannot be determined by the above description. There is > >>> no need to correlate length and number of points. Neither > >>> Euclid or Hilbert ever did that. > > >> Gee, I guess it's a novel idea, then. That might make it good, and not > >> necessarily bad. Hilbert also didn't bother to generalize his axioms to > >> include anything but Euclidean space, which is lazy. He's got too many > >> axioms, and they do too little. :) > > > Then you should not be complaining about the "set of points" approach > > to geometry and instead should be complaining about all prior approaches > > to geometry. Apparently they are all "limited" to you. Of course > > you cannot identify any actual limitation, but that is par for the course. > > I wouldn't say geometry is perfected yet. And yet you remain incapable of stating what these "limitations" are. Why is that? Could it be because you can't actually think of any? -- mike.
From: Virgil on 21 Mar 2007 16:05
In article <460184ba(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Mike Kelly wrote: > > On 21 Mar, 15:47, Tony Orlow <t...(a)lightlink.com> wrote: > >> Mike Kelly wrote: > >>> On 21 Mar, 05:47, Tony Orlow <t...(a)lightlink.com> wrote: > >>>> step...(a)nomail.com wrote: > >>>>> In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >>>>>> PD wrote: > >>>>>>> No one says a set of points IS in fact the constitution of physical > >>>>>>> object. > >>>>>>> Whether it is rightly the constitution of a mentally formed object > >>>>>>> (such as a geometric object), that seems to be an issue of > >>>>>>> arbitration > >>>>>>> and convention, not of truth. Is the concept of "blue" a correct one? > >>>>>>> PD > >>>>>> The truth of the "convention" of considering higher geometric objects > >>>>>> to > >>>>>> be "sets" of points is ascertained by the conclusions one can draw > >>>>>> from > >>>>>> that consideration, which are rather limited. > >>>>> How is it limited Tony? Consider points in a plane, where each > >>>>> point is identified by a pair of real numbers. The set of > >>>>> points { (x,y) | (x-3)^2+(y+4)^2=10 } describes a geometric object. > >>>> That's a very nice circle, Stephen, very nice.... > >>>>> In what way is this description "limited"? Can you provide a > >>>>> better description, and explain how it overcomes those limitations? > >>>> There is no correlation between length and number of points > >>> Oh. And I suppose there *is* such a correlation in "real" geometry? > >>> -- > >>> mike. > >> In my geometry |{x in R: 0<x<=1}| = Big'Un (or oo). > > > > What does that have to do with geometry? > > > > -- > > mike. > > > > It states the specific infinite number of points in the unit interval, > say, on the real line. Since TO's infinities are not like anyone else's ( longer line segments seem to have more points in TOmetry) "Big'Un" is no use to anyone else. |