The Virgin Birth of Points
in [Physics]
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From: Robert J. Kolker on 15 Nov 2007 12:49 Dave Seaman wrote: > You obviously didn't take my suggestion to look up the definition of a > vector space. I'll make it easy for you. You can find the definition at > <http://en.wikipedia.org/wiki/Vector_space>. The vectors are simply the > elements of the group called V on that page. We don't need to know > anything else about V except that it satisfies the properties stated > there. some geometrical intuition could be useful, but it is not logically necessary. Think of geometry as an Intuition Pump, in the sense that Daniel Dennett uses the term. Bob Kolker
From: Amicus Briefs on 15 Nov 2007 17:48 On Thu, 15 Nov 2007 19:29:41 +0000 (UTC), Dave Seaman <dseaman(a)no.such.host> wrote: > That is, b is the greatest lower bound of the set of cuts, which must >exist by completeness of the real numbers. That is pure philosophy and Nature abhors philosophers.
From: Dave Seaman on 15 Nov 2007 18:37 On Thu, 15 Nov 2007 15:48:48 -0700, Amicus Briefs wrote: > On Thu, 15 Nov 2007 19:29:41 +0000 (UTC), Dave Seaman ><dseaman(a)no.such.host> wrote: >> That is, b is the greatest lower bound of the set of cuts, which must >>exist by completeness of the real numbers. > That is pure philosophy and Nature abhors philosophers. That is pure mathematics. Completeness in this context means that the real numbers satisfy the least upper bound axiom, which is equivalent to the greatest lower bound axiom: every nonempty set of real numbers that is bounded below has a greatest lower bound. It is very easily proved, using the Dedekind cut definition of the real numbers. -- 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: Lester Zick on 15 Nov 2007 21:14 On Thu, 15 Nov 2007 11:18:14 -0500, "Robert J. Kolker" <bobkolker(a)comcast.net> wrote: >Lester Zick wrote: >> >> >> So do you insist space does exist or doesn't? > >Physical space. Not to be confused with mathematical space which does >not physically exist. Physical space only exists to the extent you can ascribe predicates to it defined mathematically. >Context is important. Of course it is. The problem is you want to divorce the physical world from the mathematical predicates defined of that physical world. ~v~~
From: Lester Zick on 16 Nov 2007 11:31
On Mon, 12 Nov 2007 13:05:28 -0500, "Robert J. Kolker" <bobkolker(a)comcast.net> wrote: >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. I wouldn't say the calculus is done over sets of points, Bobby. More likely "sets" of infinitesimals. ~v~~ |