The Virgin Birth of Points
in [Physics]
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From: Kenneth Doyle on 12 Nov 2007 17:00 On Mon, 12 Nov 2007 10:17:08 -0700, Lester Zick wrote: > unionizing of points Wasn't that a mafia racket that started on the waterfront? Oh, hang on, that was the unionizing of punts. Never mind.
From: Lester Zick on 12 Nov 2007 17:22 On Mon, 12 Nov 2007 10:56:00 -0800, Randy Poe <poespam-trap(a)yahoo.com> wrote: >On Nov 12, 12:15 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On Mon, 12 Nov 2007 06:48:11 -0500, "Robert J. Kolker" >> >> <bobkol...(a)comcast.net> wrote: >> >William Elliot wrote: >> >> >> Clearly points don't have zero length, they have a positive infinitesimal >> >> length for which zero is just the closest real approximation. >> >> >You don't need to resort to non-standard analysis. Within the realm of >> >standard real numbers, the matter is settle using measure (either Borel >> >or Lebesque) >> >> I wouldn't call the calculus non standard analysis. > >Calculus does not require infinitesimals or NSA. I >believe that was Leibniz's method, but we mostly >follow Newton's development which only requires >a theory of limits. So differentials are points? ~v~~
From: Lester Zick on 12 Nov 2007 17:26 On Mon, 12 Nov 2007 22:00:21 GMT, Kenneth Doyle <nobody(a)notmail.com> wrote: >On Mon, 12 Nov 2007 10:17:08 -0700, Lester Zick wrote: > >> unionizing of points > >Wasn't that a mafia racket that started on the waterfront? Oh, hang on, >that was the unionizing of punts. Never mind. Actually in the New Yorker, the unionizing of puns. ~v~~
From: Lester Zick on 12 Nov 2007 17:27 On Mon, 12 Nov 2007 13:20:13 -0500, "Robert J. Kolker" <bobkolker(a)comcast.net> wrote: >Dave Seaman wrote: >> >> >> I think you need to learn some measure theory. This is a question about >> mathematics, by the way, not philosophy. > >Zick is totally incapable of understanding either mathematics or >physics. Robert Heinlein had some clever things to say about people who >cannot cope with mathematics. Heinlein said they are subhuman but >capable of wearing shoes and keeping clean. Unlike yourself, Bobby. ~v~~
From: Robert J. Kolker on 12 Nov 2007 17:36
John Jones wrote: > A line is not a set of points because sets are indifferent to order. > However, if you care to order points we still do not have a minimal > definition of a line. Consider E2, the set of number pairs (x,y) x,y real taken as points. Along with the pythagorian metric and the obvious definition of lines (sets of (x,y) which satisfy a*x + b*y = c for some constants a,b,c) you get a structure that satistfies Hilberts postulates for plane geometric space. Since the axioms are categorica, all instances of Euclidea plane geometry (as axiomatized by Hilbert) are isometric. So a model where lines consist of points yields an instance of the geometry. Since the line can be parametrized by a single variable it can be easily ordered. Where did you get you degree? I need to know, so I won't send my kids there. Bob Kolker > |