The Definition of Points
in [Math]
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From: Tony Orlow on 13 Apr 2007 13:40 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. 01oo
From: Tony Orlow on 13 Apr 2007 13:42 Lester Zick wrote: > On Thu, 12 Apr 2007 14:23:04 -0400, Tony Orlow <tony(a)lightlink.com> > wrote: > >> 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%!!! :) > > Not exactly, Tony. 0/0 would have to be evaluated under L'Hospital's > rule. > > ~v~~ Well, you put something together that one can take a derivative of, and let's see what happens with that. 01oo
From: Tony Orlow on 13 Apr 2007 13:45 Lester Zick wrote: > On Thu, 12 Apr 2007 14:31:52 -0400, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> On Sat, 31 Mar 2007 20:51:49 -0500, Tony Orlow <tony(a)lightlink.com> >>> wrote: >>> >>>> A logical statement can be classified as true or false? True or false? >>> You show me the demonstration of your answer, Tony, because it's your >>> question and your claim not mine. >>> >>> ~v~~ >> I am asking you whether that statement is true or false. If you have a >> third answer, I'll be happy to entertain it. > > The point being, Tony, that you don't have a first answer much less a > second or third. You can't tell me or anyone else what it means to be > true in mechanically exhaustive terms. Mathematikers routinely demand > students deal in the most exacting exhaustive mechanical terms with > axioms, theorems, and doctrines of their own. Yet the moment they're > required to deal with their own axioms, doctrines, and assumptions of > truth in mechanically exhaustive terms they shy away with complaints > no one can expect to prove the truth of what they assume to be true. > > You draw up all kinds of binary "truth" tables as if they meant or had > to mean something in mechanically exhaustive terms and demand others > deal with them in binary terms you set forth. Yet you can't explain > what you mean by "truth" or "falsity" in mechanically exhaustive terms > to begin with. So how do you expect anyone to deal with truth tables? > > ~v~~ Just answer the question above. 01oo
From: MoeBlee on 13 Apr 2007 13:48 On Apr 13, 10:21 am, Tony Orlow <t...(a)lightlink.com> wrote: > MoeBlee wrote: > > On Apr 12, 12:27 pm, Tony Orlow <t...(a)lightlink.com> wrote: > >> MoeBlee wrote: > >>> On Mar 31, 5:39 am, Tony Orlow <t...(a)lightlink.com> wrote: > >>>> In order to support the notion of aleph_0, one has to discard the basic > >>>> notion of subtraction in the infinite case. That seems like an undue > >>>> sacrifice to me, for the sake of nonsense. Sorry. > >>> For the sake of a formal axiomatization of the theorems of ordinary > >>> mathematics in analysis, algebra, topology, etc. > >>> But please do let us know when you have such a formal axiomatization > >>> but one that does have cardinal subtraction working in the infinite > >>> case just as it works in the finite case. > >>> MoeBlee > >> Sorry, MoeBlee, but when I produce any final product in this area, > >> cardinality will be a footnote, and not central to the theory. As I work > >> on other things, so do I work on this. > > > I really don't care what you work on. My point is that your commentary > > in these threads has virtually no formal mathematical import, as it > > comes down to a bunch of whining that your personal notions are not > > embodied in set theory even though you can't point to a formal system > > (either published or of your own, and the gibberish you've posted in > > threads and on your own site is not even a corhernt attempt toward a > > formal system) that does embody your personal notions and you can't > > even HINT at what such a system might be. > > > MoeBlee > > What does any of your whining have to do with the definition of points? The topic (as even quoted in inclusion in this post) was broader than the mere "definition of points", whatever you mean by "definition of points". > This is tiresome. Quite so. It would be most refreshing if you replied with some actual (your terminological gibberish does not qualify) mathematics (whether standard fare or original recipe, both are welcome) for a change. MoeBlee
From: Tony Orlow on 13 Apr 2007 13:49
Lester Zick wrote: > On Thu, 12 Apr 2007 14:30:32 -0400, Tony Orlow <tony(a)lightlink.com> > wrote: > >> 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 > > What strings? Care to define what your "mappings" "between" "strings" > and "meaning" mean, Tony? Then we can get to the basis of grammar. > >>>>> 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~~ You do know what "strings" are, don't you? And grammar? And language? And, um, meaning? What's the difference between a duck? 01oo |