The Virgin Birth of Points
in [Physics]
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From: Lester Zick on 16 Nov 2007 13:37 On Thu, 15 Nov 2007 23:37:05 +0000 (UTC), Dave Seaman <dseaman(a)no.such.host> wrote: >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. But you can't demonstrate any of this is true. That makes it philosophy. ~v~~
From: Amicus Briefs on 17 Nov 2007 12:01 On Fri, 16 Nov 2007 11:26:19 -0800 (PST), PD <TheDraperFamily(a)gmail.com> wrote: >On Nov 16, 12:37 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On Thu, 15 Nov 2007 23:37:05 +0000 (UTC), Dave Seaman >> >> <dsea...(a)no.such.host> wrote: >> >On Thu, 15 Nov 2007 15:48:48 -0700, Amicus Briefs wrote: >> >> On Thu, 15 Nov 2007 19:29:41 +0000 (UTC), Dave Seaman >> >><dsea...(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. >> >> But you can't demonstrate any of this is true. That makes it >> philosophy. > >On the contrary -- he just mentioned the proof of a theorem. I believe "true" was mentioned as opposed to mere "conviction". >Now, demonstration to the point of convincing you is an entirely >different matter. In most cases, a mathematical or a logical proof >requires only that someone reasonably conversant with the terms and >notation used in the proof can follow it and concur. It is not >necessary to additionally require that a dead tree stump also be >convinced of the truth of the proof. If you are having difficulty >following a published proof that is recognized to be followable by the >average reader, then you have to ask yourself in what ways you are >closer to a dead tree stump than you are to the average reader. > >PD
From: Lester Zick on 17 Nov 2007 13:08 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 between points. The points over which integrals are taken are immaterial because integrals are taken with infinitesimals not points just as the converse differential operation yields infinitesimals not points. ~v~~
From: Amicus Briefs on 17 Nov 2007 13:32 On Sat, 17 Nov 2007 09:30:33 -0800 (PST), PD <TheDraperFamily(a)gmail.com> wrote: >> >> >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. >> >> >> But you can't demonstrate any of this is true. That makes it >> >> philosophy. >> >> >On the contrary -- he just mentioned the proof of a theorem. >> >> I believe "true" was mentioned as opposed to mere "conviction". > >And as I intimated, something being true does not imply that a dead >tree stump will be convinced of its truth. If something is indeed >true, but you find yourself unconvinced of the truth, then consider, >Mr. Zick, in what ways you are closer to a dead tree stump than to the >average reader. > >You have demonstrated a deep and pervasive ability to be unconvinced >of the simplest things, things that the average reader finds both >compelling and understandable. Your inability to follow these simple >things does not speak to the truth of those things so much as to your >ability to recognize truth when it is standing right there in front of >you. So "dead tree stumps", "conviction", "deep and pervasive ability to be convinced", and "compelling and understandable to the average reader" are your criteria of "truth"? Maybe that's why it's called philosophy.
From: Lester Zick on 18 Nov 2007 20:07
On Sun, 18 Nov 2007 16:20:43 -0800 (PST), Randy Poe <poespam-trap(a)yahoo.com> wrote: >We are not in agreement. You haven't yet said a >statement I agree with in your entire posting >history. Everybody's wrong but Randy. Randy and his scriptures are perfect. It's the siege mentality of empirics.Empirics have no way to tell what is true so they have to assume they are and thus no one else can be. Can anyone say "paranoia"? ~v~~ |