The Virgin Birth of Points
in [Physics]
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From: Robert J. Kolker on 12 Nov 2007 13:23 Igor wrote: > > > No. Your main purpose in this thread is the same as in any other of > your threads. And that is the intentional obfuscation of established > mathematical concepts. > > He is unable to do otherwise. He cannot comprehend standard mathematical concepts. Zick cannot cope with mathematics. Robert Heinlein had some interesting things to say about people like Zick. Bob Kolker > > >
From: Hero on 12 Nov 2007 13:48 Randy wrote: > Hero wrote: > > Robert wrote: > > > Lester Zick wrote: .. > > > > The Virgin Birth of Points > > > > ~v~~ > > > > > The Jesuit heresy maintains points have zero length but are not of > > > > zero length and if you don't believe that you haven't examined the > > > > argument closely enough. .. > > > In Euclidean space a set which has exactly one pont as a member has > > > measure zero. But you can take the union of an uncountable set of such > > > singleton sets and get a set with non-zero measure. .. > > What measure will give a non-zero number/value? .. > The Lebesgue measure of the interval [0,1] is 1. The > Lebesgue measure of every finite and countable subset > of that interval is 0. The Lebesgue measure of the Cantor > set, which is uncountable, is also 0. > > Is that what you were asking? .. Yes.Thanks, Randy. And thanks to Dave, John and Robert too. Now we have all we need to point to the important fact: It is measuring sets of points, not measuring points or measuring many points. A point A is different from the set { A }. And a hint to the standard topology of the real number line, which according to Kuratowski, gives to every two points the intervall in between, a set of points. With friendly greetings Hero
From: Dave Seaman on 12 Nov 2007 13:54 On Mon, 12 Nov 2007 13:20:13 -0500, Robert J. Kolker 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. Zick is in my killfile. He is not the person I was responding to. -- Dave Seaman Oral Arguments in Mumia Abu-Jamal Case heard May 17 U.S. Court of Appeals, Third Circuit <http://www.abu-jamal-news.com/>
From: Randy Poe on 12 Nov 2007 13:56 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. - Randy
From: John Jones on 12 Nov 2007 14:31
On Nov 12, 6:05?pm, Dave Seaman <dsea...(a)no.such.host> wrote: > On Mon, 12 Nov 2007 07:50:52 -0800, John Jones wrote: > > On Nov 12, 3:42?pm, Dave Seaman <dsea...(a)no.such.host> wrote: > >> On Mon, 12 Nov 2007 07:06:39 -0800, Hero wrote: > >> > Robert wrote: > >> >> Lester Zick wrote: > >> >> > The Virgin Birth of Points > >> >> > ~v~~ > > >> >> > The Jesuit heresy maintains points have zero length but are not of > >> >> > zero length and if you don't believe that you haven't examined the > >> >> > argument closely enough. > > >> >> In Euclidean space a set which has exactly one pont as a member has > >> >> measure zero. But you can take the union of an uncountable set of such > >> >> singleton sets and get a set with non-zero measure. > > >> > What measure will give a non-zero number/value? > > >> Lebesgue measure will do so, not for all possible uncountable sets, but > >> for some. For example, the Lebesgue measure of an interval [a,b] is its > >> length, b-a. > > >> -- > >> Dave Seaman > >> Oral Arguments in Mumia Abu-Jamal Case heard May 17 > >> U.S. Court of Appeals, Third Circuit > >> <http://www.abu-jamal-news.com/> > > An interval [a,b] is composed of positions, not points. But even > > positions are constructions, and it is not appropriate to analyse a > > construction in spatial terms. > > I think you need to learn some measure theory. This is a question about > mathematics, by the way, not philosophy. > > -- > Dave Seaman > Oral Arguments in Mumia Abu-Jamal Case heard May 17 > U.S. Court of Appeals, Third Circuit > <http://www.abu-jamal-news.com/>- Hide quoted text - > > - Show quoted text - I think you need to distinguish between a position and a point before wildly conflating them in both a philosophical and mathematical confusion. |