The Virgin Birth of Points
in [Physics]
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From: Lester Zick on 12 Nov 2007 12:19 On Mon, 12 Nov 2007 06:46:26 -0500, "Robert J. Kolker" <bobkolker(a)comcast.net> 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. So if you unionize an infinite number of points, would the converse operation be decertification of the union and wouldn't that constitute division by zero? ~v~~
From: Robert J. Kolker on 12 Nov 2007 13:04 Lester Zick wrote: > > Except the main purpose of this thread is less to discuss the zero > length of points than the heresy of maintaining self contradictory > predicates, as in "has zero length" and "is not of zero length". Points do not have a length (0 or not). Some -sets- of points have -measure-. In particular a set consisting of a single point has measure 0. You have manage to confuse an object with a set whose element is that object. Bob Kolker
From: Dave Seaman on 12 Nov 2007 13:05 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/>
From: Robert J. Kolker on 12 Nov 2007 13:05 Lester Zick wrote: > > I wouldn't call the calculus non standard analysis. Integrals are done over sets of points, not idividual points. Learn to distinguish between sets and the elements of the sets. Bob Kolker
From: Robert J. Kolker on 12 Nov 2007 13:06
Lester Zick wrote: > > > Then I'm curious about this unionizing of points people talk about. You are curious about sets (and no wonder, you know nothing about them). Bob Kolker |