The Definition of Points
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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
From: Lester Zick on 23 Mar 2007 12:50
On Thu, 22 Mar 2007 20:14:43 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On 22 Mar 2007 11:12:40 -0700, "PD" <TheDraperFamily(a)gmail.com> wrote: >> >>> On Mar 22, 12:28 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >>>> On Wed, 21 Mar 2007 22:24:22 -0500, Tony Orlow <t...(a)lightlink.com> >>>> wrote: >> >> >>>>> Lester Zick wrote: >>>>>> On Wed, 21 Mar 2007 07:40:46 -0400, Bob Kolker <nowh...(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~~ >>>>> Purrrrr....say! Division by zero is not undefinable. One just has to >>>>> define zero as a unit, eh? >>>> A unit of what, Tony? >>>> >>>>> Uncountable bunches certainly can attain nonzero measure. :) >>>> Uncountable bunches of zeroes are still zero, Tony. >>>> >>> Why no, no they're not, Lester. >> >> Of course you say so, Draper. Fact is that uncountable bunches of >> infinitesimals are not zero but non uncountable bunches of zeroes are. >> > >"zero" and "infinitesimal" are often used interchangeably, Not by mathematicians they're not. That's why you can have a zero and 0 dr. Huge difference. > but they >really mean slightly different things, as I learned early on here. Definitely not from mathematikers. They spend all their time talking about arithmetic and arithmetic SOAP "models". >>> Perhaps a course in real analysis would be of value. >> >> And perhaps a course in truth would be of value to you unless of >> course you wish to maintain that division by zero is defined even in >> neomethematics. >> > >It should be, on each level of relatively infinite scale... On a infinitesimal scale perhaps. Not on a scale on zero. There is no scale on zero. That's exactly why division by zero is not defined even in neomathematics. Contrary to the fond hopes and desires of those looking to integrate points into lines. Yeah. Good luck with that one. >>> Ever consider reading, rather than just making stuff up? >> >> No. ~v~~ |