The Definition of Points
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From: Lester Zick on 1 Apr 2007 20:46 On Sat, 31 Mar 2007 19:56:38 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Fri, 30 Mar 2007 12:25:24 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >>>> wrote: >>>> >>>>>>> If n is >>>>>>> infinite, so is 2^n. If you actually perform an infinite number of >>>>>>> subdivisions, then you get actually infinitesimal subintervals. >>>>>> And if the process is infinitesimal subdivision every interval you get >>>>>> is infinitesimal per se because it's the result of a process of >>>>>> infinitesimal subdivision and not because its magnitude is >>>>>> infinitesimal as distinct from the process itself. >>>>> It's because it's the result of an actually infinite sequence of finite >>>>> subdivisions. >>>> And what pray tell is an "actually infinite sequence"? >>>> >>>>> One can also perform some infinite subdivision in some >>>>> finite step or so, but that's a little too hocus-pocus to prove. In the >>>>> meantime, we have at least potentially infinite sequences of >>>>> subdivisions, increments, hyperdimensionalities, or whatever... >>>> Sounds like you're guessing again, Tony. >>>> >>>> ~v~~ >>> An actually infinite sequence is one where there exist two elements, one >>> of which is an infinite number of elements beyond the other. >> >> Which tells us what exactly, Tony, infinite sequences are infinite? >> >> ~v~~ > >It tells us "actual" means "uncountable" in the context of "infinite". Same difference I expect if we don't understand what you mean by "infinite". ~v~~
From: Lester Zick on 1 Apr 2007 20:50 On Sun, 01 Apr 2007 07:11:42 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >T. O wrote. >> One may express them algebraically, but their truth is derived and >> justified geometrically. > >There is only one justification in mathematics. Does the conclusion >follow logically from the premises. Not actually, Bob. That's pure Aristotelian syllogistic inference not mathematics. ~v~~
From: Lester Zick on 1 Apr 2007 20:54 On Sun, 01 Apr 2007 07:14:57 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Tony Orlow wrote: > >> >> >> Bob - wake up. How do we know relativity is correct? Because it follows >> from e=mc^2? > >Correct in what sense. Mathematically, relativity theory is simply an >excercise in Poincare groups. As a physics theory, we insist on >empirical corroberation of the conclusions that are interpreted to say >something about the world. Conventional mathematics says nothing whatsoever about the world, Bob, as you call. Quite possibly I'm the first to demonstrate what can be proven of the real world logically and mathematically. The rest is only your imagination and assumptions of truth about the real world. ~v~~
From: Lester Zick on 1 Apr 2007 21:02 On Sat, 31 Mar 2007 21:14:27 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Yeah, "true" and "false" and "or" are kinda ambiguous, eh?" They are where your demonstrations of their truth are concerned because there don't seem to be any. You just trot them out as if they were obvious axiomatic assumptions of truth not requiring any mechanical basis whatsoever or demonstrations on your part. ~v~~
From: Lester Zick on 1 Apr 2007 21:04
On Sat, 31 Mar 2007 21:14:27 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >>> You need to define what relation your grammar denotes, or there is no >>> understanding when you write things like "not a not b". What grammar did you have in mind exactly, Tony? >> Of course not. I didn't intend for my grammar to denote anything in >> particular much as Brian and mathematikers don't intend to do much >> more than speak in tongues while they're awaiting the second coming. >> > >Then, what, you're not actually saying anything? Of course I am. ~v~~ |