The Definition of Points
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From: Lester Zick on 22 Mar 2007 13:42 On Wed, 21 Mar 2007 22:39:56 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Virgil wrote: >> 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. > >Only by wielding the tool do we gauge its utility. Certainly true, Tony, and a good observation. ~v~~
From: Virgil on 22 Mar 2007 13:44 In article <4602b106(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Mike Kelly wrote: > > > > Firstly, the continuum hypothesis is nothing to do with geometry. > > It does, if sets are combined with measure and a geometrical > representation of the question considered. The CH still has nothing directly to do with geometry. > Is half an infinity less than > itself? Geometrically, yes, the reals in (0,1] are half the reals in (0,2]. Not in any sense recognized by the CH. > > > > > Secondly, division is not defined for infinite cardinal numbers. > > I'm not interested in cardinality, but a richer system of infinities, > thanks. Which supposedly richer system is still so poor that it it does not exist. Other than as one of TO's pipe dreams.
From: Lester Zick on 22 Mar 2007 13:44 On Wed, 21 Mar 2007 22:40:03 -0600, Virgil <virgil(a)comcast.net> wrote: >Since TO's tool seems to be unwieldable, in any practical way, even by >himself, we gauge it to be of no utility to anyone else. Are my tools unwieldable, Virgil? If so perhaps you'd care to explain how so? Or not. Probably not since you're pretty much stuck on stupid. ~v~~
From: Lester Zick on 22 Mar 2007 13:49 On Wed, 21 Mar 2007 22:42:22 -0600, Virgil <virgil(a)comcast.net> wrote: >TO teaching Zick is like the blind leading the blind, re mathematics. Or in your case the halt leading the lame. Very lame. ~v~~
From: Lester Zick on 22 Mar 2007 13:54
On Wed, 21 Mar 2007 20:43:22 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >This view of mathematics as empirical content free is a relatively >modern view. So what about the axioms, Bob? Are they empirical or just false? > In the beginning, mathematics was thought to be talking >about the world. It still is. > But Euclidean geometry can't be -true- in the factual >sense since there are non-Euclidean. And is Euclidean geometry a limiting case and without Euclidean geometry are non Euclidean geometries true? > Euclidean geometry is readily >-applied- to flat spaces with a straightforward pythagorean metric. And without Euclidean geometry non Euclidean geometries aren't applicable to anything. ~v~~ |