The Definition of Points
in [Math]
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From: Lester Zick on 22 Mar 2007 18:59 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. >>> 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. >>> 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? Or do you think straight lines reside on curves? Or do you think pi resides on both and a circle is equal to straight line approximations? 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. >> 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~~
From: Lester Zick on 22 Mar 2007 19:04 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. >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. >Ever consider reading, rather than just making stuff up? No. ~v~~
From: stephen on 22 Mar 2007 19:04 In sci.math Tony Orlow <tony(a)lightlink.com> wrote: > Mike Kelly wrote: >> >> You brought up the continuum hypothesis. Next post, you say you don't >> want to talk about cardinality. Risible. > CH is a question in ZFC. The answer lies outside ZFC. Just like the answer to Fermat's Last Theorem lies outside the integers. Stephen
From: Lester Zick on 22 Mar 2007 19:05 On Thu, 22 Mar 2007 17:15:35 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Wed, 21 Mar 2007 22:24:22 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> Lester Zick wrote: >>>> 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~~ >>> 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. >> >> ~v~~ > >Infinitesimal units can be added such that an infinite number of them >attain finite sums. And since when exactly, Tony, do infinitesimals equal zero pray tell? ~v~~
From: Lester Zick on 22 Mar 2007 19:10
On 22 Mar 2007 09:57:31 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: > What does asserting that do for us? Not much. Probably as much as asserting that so many straight line segments constitute a straight line or that there is a real number line or an undefined number of points make up a line segment or a line is made up of points or tables are made up of beer bottles. Six of one, half dozen of the other. Or more likely none of both. ~v~~ |