The Definition of Points
in [Math]
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From: Bob Cain on 23 Mar 2007 05:16 Lester Zick wrote: > You know I'm beginning to get the distinctly unpleasant impression > your putatuve psychological expose of me is more self portrait than > anything else. The rest of us, that consensus you believe it your mission to tweak, consider PD's sketch a very witty and perfectly appropriate portrait of you and your vanity threads, Lester. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein
From: Brian Chandler on 23 Mar 2007 05:28 Tony Orlow wrote: > Mike Kelly wrote: > > On 22 Mar, 21:42, Tony Orlow <t...(a)lightlink.com> wrote: > >> Mike Kelly wrote: > >>> On 22 Mar, 16:38, Tony Orlow <t...(a)lightlink.com> wrote: > >>>> Mike Kelly wrote: > >>>>> On 22 Mar, 13:03, Tony Orlow <t...(a)lightlink.com> wrote: > >>>>>> Mike Kelly wrote: > >>>>>>> On 22 Mar, 03:28, Tony Orlow <t...(a)lightlink.com> wrote: > >>>>>>>> Mike Kelly wrote: > >>>>>>>>> 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: <snippi, snippa> > > Risible. > > > > -- > > mike. > > > > Riete! Cosa? Vuoi dire per caso 'ridete'? > antonio. Right, keep taking the tablets. Brian Chandler http://imaginatorium.org
From: Randy Poe on 23 Mar 2007 07:48 On Mar 22, 9:03 pm, Tony Orlow <t...(a)lightlink.com> wrote: > Virgil wrote: > > Which supposedly richer system is still so poor that it it does not > > exist. Other than as one of TO's pipe dreams. > > Not yet as a complete replacement for ZFC, but that wasn't built i na > day, or a few years, either. > But, like Rome and unlike TO-matics, the builders could look around every once in awhile and say "this has grown since last time I looked." - Randy
From: Lester Zick on 23 Mar 2007 12:42 On Thu, 22 Mar 2007 20:12:02 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Thu, 22 Mar 2007 17:14:38 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Wed, 21 Mar 2007 22:45:54 -0500, Tony Orlow <tony(a)lightlink.com> >>>> wrote: >>>> >>>>> Lester Zick wrote: >>>>>> On Wed, 21 Mar 2007 14:17:16 -0500, Tony Orlow <tony(a)lightlink.com> >>>>>> wrote: >>>>>> >>>>>>> It states the specific infinite number of points in the unit interval, >>>>>>> say, on the real line. >>>>>> And what real line would that be, Tony? >>>>>> >>>>>> ~v~~ >>>>> The one that fully describes the real numbers. >>>> You mean a straight line that describes curves exactly? Or some curve >>>> that describes straight lines exactly? >>>> >>> There is no straight line, but only the infinitesimally curved. :D >> >> What evidence do you have to support your opinion, Tony? Straight >> lines have zero curvature. >> > >What evidence would you like for the difference between zero and an >infinitesimal? Not something finite, I hope.... What evidence would you like for the difference between zero and i, Tony? >>>>> Like, duh! The one that >>>>> exists. >>>> Except there is no such line, Tony. At least none that describes both >>>> curves and straight lines together exactly.And if you don't believe me >>>> Bob Kolker has acknowledged the point previously. >>>> >>> Well, if Bob says so, then.... >> >> I might agree if Bob hadn't gone out of his way to say so. It was >> uncharacteristic of him to say so. But the very fact that he could see >> so and said so inclines me to his opinion rather than yours. >> > >So be it. > >>>>> E R >>>>> 0eR >>>>> 1eR >>>>> 0<1 >>>>> xeR ^ yeR ^ x<y -> EzeR x<z ^ z<y >>>> Very fanciful, Tony. You mean if you know the approximation for pi >>>> lies between 3 and 4 on a straight line pi itself does too? >>> For instance. If you can get arbitrarily close to pi without leaving the >>> line, then it resides on the line. Otherwise it would be some distance >>>from the line, and there would be a lower limit to your approximation. >> >> What makes you think pi resides on straight lines instead of circles? > >It is between 3 and 4. The problem is that approximations to pi reside on straight lines but their limit does not. Pi resides on circular arcs or curves.And before Randy/Stephen/Virgil can pop in to ask what I mean by "reside" I suggest they try to "point out" pi on a straight line whilst I "point out" pi on a circle. >> Or do you think straight lines reside on curves? > >They may intersect... Sure. But that doesn't point out pi on a straight line. Hence there is no real number line. >Or do you think pi >> resides on both and a circle is equal to straight line approximations? > >An infinitely regressive one, perchance. No, Tony. Here you're definitely wrong. Approximations to pi lie on a straight line but their limit lies on a circular arc or curve. >> Otherwise it would indeed be at some distance from the straight line >> and there would be no point on the straight line corresponding to pi. >> > >Then one could not point out arbitrarily close points to the desired >irrational or transcendental, which all reside on the line. The distance >from that point to the line would be some lower limit. But it's never on the straight line. It's always on a circular arc. >>>> You see, Tony, this is the basic reason I refuse to be drawn into >>>> discussion on collateral mathematical issues as interesting as they >>>> might be. I can't even get the most elementary point across even to >>>> those supposedly paying attention to what I say. >>>> >>>> ~v~~ >>> Try me. >> >> Already have. Don't know what else to say. >> >> ~v~~ > >You'll think of something. I'm sure you will, Tony. ~v~~
From: Randy Poe on 23 Mar 2007 12:49
On Mar 23, 12:42 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > On Thu, 22 Mar 2007 20:12:02 -0500, Tony Orlow <t...(a)lightlink.com> > wrote: > > > > >Lester Zick wrote: > >> On Thu, 22 Mar 2007 17:14:38 -0500, Tony Orlow <t...(a)lightlink.com> > >> wrote: > > >>> Lester Zick wrote: > >>>> On Wed, 21 Mar 2007 22:45:54 -0500, Tony Orlow <t...(a)lightlink.com> > >>>> wrote: > > >>>>> Lester Zick wrote: > >>>>>> On Wed, 21 Mar 2007 14:17:16 -0500, Tony Orlow <t...(a)lightlink.com> > >>>>>> wrote: > > >>>>>>> It states the specific infinite number of points in the unit interval, > >>>>>>> say, on the real line. > >>>>>> And what real line would that be, Tony? > > >>>>>> ~v~~ > >>>>> The one that fully describes the real numbers. > >>>> You mean a straight line that describes curves exactly? Or some curve > >>>> that describes straight lines exactly? > > >>> There is no straight line, but only the infinitesimally curved. :D > > >> What evidence do you have to support your opinion, Tony? Straight > >> lines have zero curvature. > > >What evidence would you like for the difference between zero and an > >infinitesimal? Not something finite, I hope.... > > What evidence would you like for the difference between zero and i, > Tony? > > > > >>>>> Like, duh! The one that > >>>>> exists. > >>>> Except there is no such line, Tony. At least none that describes both > >>>> curves and straight lines together exactly.And if you don't believe me > >>>> Bob Kolker has acknowledged the point previously. > > >>> Well, if Bob says so, then.... > > >> I might agree if Bob hadn't gone out of his way to say so. It was > >> uncharacteristic of him to say so. But the very fact that he could see > >> so and said so inclines me to his opinion rather than yours. > > >So be it. > > >>>>> E R > >>>>> 0eR > >>>>> 1eR > >>>>> 0<1 > >>>>> xeR ^ yeR ^ x<y -> EzeR x<z ^ z<y > >>>> Very fanciful, Tony. You mean if you know the approximation for pi > >>>> lies between 3 and 4 on a straight line pi itself does too? > >>> For instance. If you can get arbitrarily close to pi without leaving the > >>> line, then it resides on the line. Otherwise it would be some distance > >>>from the line, and there would be a lower limit to your approximation. > > >> What makes you think pi resides on straight lines instead of circles? > > >It is between 3 and 4. > > The problem is that approximations to pi reside on straight lines but > their limit does not. Pi resides on circular arcs or curves.And before > Randy/Stephen/Virgil can pop in to ask what I mean by "reside" I > suggest they try to "point out" pi on a straight line whilst I "point > out" pi on a circle. I'm going to ask what you mean by "point out" and why it is necessary to existence. - Randy |