The Definition of Points
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From: Tony Orlow on 13 Apr 2007 15:27 Virgil wrote: > In article <461fc017(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> MoeBlee wrote: >>> On Apr 12, 2:36 pm, "MoeBlee" <jazzm...(a)hotmail.com> wrote: >>> >>>> Zermelo's motivation was to prove that every set is well ordered. >>> Since that phrasing might be misunderstood, I should say that I mean: >>> Zermelo's motivation was to prove that for every set, there exists a >>> well ordering on it. >>> >>> MoeBlee >>> >> I am not sure how the Axiom of Choice demonstrates that. >> >> Well Order the Reals! > > TO misses the point again. Existence proofs do not have to actually > instantiate what they are proving exists. > > And the AOC allows an existence proof of a well ordering of any set > without requiring that any such well orderings be actually created. How convenient!!! :D
From: Lester Zick on 13 Apr 2007 15:27 On Fri, 13 Apr 2007 13:40:24 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Thu, 12 Apr 2007 14:12:56 -0400, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Sat, 31 Mar 2007 18:05:25 -0500, Tony Orlow <tony(a)lightlink.com> >>>> wrote: >>>> >>>>> Lester Zick wrote: >>>>>> On Fri, 30 Mar 2007 12:06:42 -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: >>>>>>>> >>>>>>>>>>> You might be surprised at how it relates to science. Where does mass >>>>>>>>>>> come from, anyway? >>>>>>>>>> Not from number rings and real number lines that's for sure. >>>>>>>>>> >>>>>>>>> Are you sure? >>>>>>>> Yes. >>>>>>>> >>>>>>>>> What thoughts have you given to cyclical processes? >>>>>>>> Plenty. Everything in physical nature represents cyclical processes. >>>>>>>> So what? What difference does that make? We can describe cyclical >>>>>>>> processes quite adequately without assuming there is a real number >>>>>>>> line or number rings. In fact we can describe cyclical processes even >>>>>>>> if there is no real number line and number ring. They're irrelevant. >>>>>>>> >>>>>>>> ~v~~ >>>>>>> Oh. What causes them? >>>>>> Constant linear velocity in combination with transverse acceleration. >>>>>> >>>>>> ~v~~ >>>>> Constant transverse acceleration? >>>> What did I say, Tony? Constant linear velocity in combination with >>>> transverse acceleration? Or constant transverse acceleration? I mean >>>> my reply is right there above yours. >>>> >>>> ~v~~ >>> If the transverse acceleration varies, then you do not have a circle. >> >> Of course not. You do however have a curve. >> >> ~v~~ > >I thought you considered the transverse acceleration to vary >infinitesimally, but that was a while back... Still do, Tony. How does that affect whether you have a curve or not? Transverse a produces finite transverse v which produces infinitesimal dr which "curves" the constant linear v infinitesimally. ~v~~
From: Lester Zick on 13 Apr 2007 15:31 On Fri, 13 Apr 2007 13:40:55 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Thu, 12 Apr 2007 14:16:11 -0400, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>>>> 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" >> >> I'm not sure that's a big help, Tony. You have yet to show there is >> any such number. >> >> ~v~~ > >How many reals between 0 and 1? That's the number. As it stands there are only two reals, one at each end. When you bisect the line there become more. It looks to me like you imagine what you're supposed to be demonstrating and then calling that infinity as if it were already there when it's not. ~v~~
From: Lester Zick on 13 Apr 2007 15:32 On Fri, 13 Apr 2007 16:10:39 +0100, Alan Smaill <smaill(a)SPAMinf.ed.ac.uk> wrote: >Lester Zick <dontbother(a)nowhere.net> writes: > >> On Thu, 12 Apr 2007 14:23:04 -0400, Tony Orlow <tony(a)lightlink.com> >> wrote: >>> >>>That's okay. 0 for 0 is 100%!!! :) >> >> Not exactly, Tony. 0/0 would have to be evaluated under L'Hospital's >> rule. > >Dear me ... L'Hospital's rule is invalid. What ho? Surely you jest! Was it invalid when I used it in college? ~v~~
From: Lester Zick on 13 Apr 2007 15:37
On 13 Apr 2007 11:24:48 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >On Apr 13, 10:56 am, Tony Orlow <t...(a)lightlink.com> wrote: >> Well, of course, Moe's technically right, though I originally asked >> Lester to define his meaning in relation to his grammar. Technically, >> grammar just defines which statements are valid, to which specific >> meanings are like parameters plugged in for the interpretation. > >That is completely wrong. You have it completely backwards. What you >just mentioned is part of semantics not grammar. Grammar is syntax - >the rules for formation of certain kinds of strings of symbols, >formulas, sentences, and other matters related purely to the >"manipulation" of sequences of symbols and sequences of formulas, and >of such objects. On the other hand, semantics is about the >interpretations, the denotations, the meanings of the symbols, strings >of symbols, formulas, sentences, and sets of sentences. Mathematical >logic includes the study of these two things - syntax and semantics - >both separately and in relation to each other. > >> I asked >> the question originally using truth tables to avoid all that, so that we >> can directly equate Lester's grammar with the common grammar, on that >> level, and derive whether "not a not b" and "not a or not b" were the >> same thing. They seem to be. > >Truth tables are basically a semantical matter. Inspection of a truth >table reveals the truth or falsehood of a sentential formula per each >of the assigments of denotations of 'true' or 'false' to the sentence >letters in the formula. If any and all these things are not demonstrably true and merely represent so many assumptions of truth why would anyone care what you think about what they are or aren't? I mean it really isn't as if truth is on your side to the exclusion of what others claim, Moe(x). ~v~~ |