The Definition of Points
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From: Tony Orlow on 12 Apr 2007 14:16 Lester Zick wrote: > On 31 Mar 2007 16:56:16 -0700, "Mike Kelly" > <mikekellyuk(a)googlemail.com> wrote: > >> On 1 Apr, 00:36, Tony Orlow <t...(a)lightlink.com> wrote: >>> Lester Zick wrote: >>>> On Fri, 30 Mar 2007 12:10:12 -0500, Tony Orlow <t...(a)lightlink.com> >>>> wrote: >>>>> Lester Zick wrote: >>>>>> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <t...(a)lightlink.com> >>>>>> wrote: >>>>>>>>> Their size is finite for any finite number of subdivisions. >>>>>>>> And it continues to be finite for any infinite number of subdivisions >>>>>>>> as well.The finitude of subdivisions isn't related to their number but >>>>>>>> to the mechanical nature of bisective subdivision. >>>>>>> Only to a Zenoite. Once you have unmeasurable subintervals, you have >>>>>>> bisected a finite segment an unmeasurable number of times. >>>>>> Unmeasurable subintervals? Unmeasured subintervals perhaps. But not >>>>>> unmeasurable subintervals. >>>>>> ~v~~ >>>>> Unmeasurable in the sense that they are nonzero but less than finite. >>>> Then you'll have to explain how the trick is done unless what you're >>>> really trying to say is dr instead of points resulting from bisection. >>>> I still don't see any explanation for something "nonzero but less than >>>> finite". What is it you imagine lies between bisection and zero and >>>> how is it supposed to happen? So far you've only said 1/00 but that's >>>> just another way of making the same assertion in circular terms since >>>> you don't explain what 00 is except through reference to 00*0=1. >>>> ~v~~ >>> But, I do. >>> >>> I provide proof that there exists a count, a number, which is greater >>> than any finite "countable" number, for between any x and y, such that >>> x<y, exists a z such that x<z and z<y. No finite number of intermediate >>> points exhausts the points within [x,z], no finite number of >>> subdivisions. So, in that interval lie a number of points greater than >>> any finite number. Call |R in (0,1]| "Big'Un" or oo., and move on to the >>> next conclusion....each occupies how m,uch of that interval? >>> >>> 01oo >> So.. you (correctly) note that there are not a finite "number" of >> reals in [0,1]. You think this "proves" that there exists an infinite >> "number". Why? (And, what is your definition of "number")? > > And what is your definition of "infinite"? > > ~v~~ "greater than any finite" 01oo
From: Virgil on 12 Apr 2007 14:22 In article <461e7764(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Lester Zick wrote: > > And what is your definition of "infinite"? > > > > ~v~~ > > "greater than any finite" > And is TO's definition of finite "less than infinite"?
From: Tony Orlow on 12 Apr 2007 14:23 Lester Zick wrote: > On Sat, 31 Mar 2007 16:18:16 -0400, Bob Kolker <nowhere(a)nowhere.com> > wrote: > >> Lester Zick wrote: >> >>> Mathematikers still can't say what an infinity is, Bob, and when they >>> try to they're just guessing anyway. So I suppose if we were to take >>> your claim literally we would just have to conclude that what made >>> physics possible was guessing and not mathematics at all. >> Not true. Transfite cardinality is well defined. > > I didn't say it wasn't, Bob. You can do all the transfinite zen you > like. I said "infinity". > >> In projective geometry points at infinity are well defined (use >> homogeneous coordinates). > > That's nice, Bob. > >> You are batting 0 for n, as usual. > > Considerably higher than second guessers. > > ~v~~ That's okay. 0 for 0 is 100%!!! :) 01oo
From: Tony Orlow on 12 Apr 2007 14:29 Lester Zick wrote: > 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~~ So, you're not interested in classifying certain propositions as "true" and others as "false", so each is either true "or" false? I coulda swored you done said that....oh nebbe mine! 01oo
From: Tony Orlow on 12 Apr 2007 14:30
Lester Zick wrote: > 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? Some commonly understood mapping between strings and meaning, basically. Care to define what your strings mean? :)1oo > >>> 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~~ |