The Definition of Points
in [Math]
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From: Tony Orlow on 17 Apr 2007 12:18 MoeBlee wrote: > On Apr 13, 12:11 pm, Tony Orlow <t...(a)lightlink.com> wrote: >> I had said that, hoping you might give some explanation, but you didn't >> really. > > Since you posted that, I wrote a long post about the axiom of choice. > Now it's not showing up in the list of posts. Darn! I went into a lot > of detail and answered your questions; I don't want to write it all > again; maybe it will show up delayed. > > MoeBlee > > That's too bad. Thanks for your effort, and sorry it's taken several days to respond. TOEKnee
From: Tony Orlow on 17 Apr 2007 12:20 Lester Zick wrote: > On Fri, 13 Apr 2007 13:45:46 -0400, Tony Orlow <tony(a)lightlink.com> > wrote: > >> 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. > > What question? You seem to think there is a question apart from > whether a statement is true or false. All your classifications rely on > that presumption. But you can't tell me what it means to be true or > false so I don't know how to answer the question in terms that will > satisfy you. > > ~v~~ A logical statement can be classified as true or false? True or false? In other words, is there a third option, for this or any other statement? 01oo
From: Tony Orlow on 17 Apr 2007 12:20 Lester Zick wrote: > On Fri, 13 Apr 2007 14:33:20 -0400, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> On Thu, 12 Apr 2007 14:35:36 -0400, Tony Orlow <tony(a)lightlink.com> >>> wrote: >>> >>>> Lester Zick wrote: >>>>> On Sat, 31 Mar 2007 20:58:31 -0500, Tony Orlow <tony(a)lightlink.com> >>>>> wrote: >>>>> >>>>>> How many arguments do true() and false() take? Zero? (sigh) >>>>>> Well, there they are. Zero-place operators for your dining pleasure. >>>>> Or negative place operators, or imaginary place operators, or maybe >>>>> even infinite and infinitesimal operators. I'd say the field's pretty >>>>> wide open when all you're doing is guessing and making assumptions of >>>>> truth. Pretty much whatever you'd want I expect.Don't let me stop you. >>>>> >>>>> ~v~~ >>>> Okay, so if there are no parameters to the function, you would like to >>>> say there's an imaginary, or real, or natural, or whatever kind of >>>> parameter, that doesn't matter? Oy! It doesn't matter. true() and >>>> false() take no parameters at all, and return a logical truth value. >>>> They are logical functions, like not(x), or or(x,y) and and(x,y). Not >>>> like not(). That requires a logical parameter to the function. >>> Tony, you might just as well be making all this up as you go along >>> according to what seems reasonable to you. My point was that you have >>> no demonstration any of these characteristics in terms of one another >>> which proves or disproves any of these properties in mechanical terms >>> starting right at the beginning with the ideas of true and false. >>> >>> ~v~~ >> Sorry, Lester, but that's an outright lie. I clearly laid it out for >> you, starting with only true and false, demonstrating how not(x) is the >> only 1-place operator besides x, true and false, and how the 2-place >> operators follow. For someone who claims to want mechanical ground-up >> derivations of truth, you certainly seem unappreciative. > > Only because you're not doing a ground up mechanical derivation of > true or false. You're just telling me how you employ the terms true > and false in particular contexts whereas what I'm interested in is how > true and false are defined in mechanically reduced exhaustive terms. > What you clearly laid out are the uses of true and false with respect > to one another once established. But you haven't done anything to > establish true and false themselves in mechanically exhaustive terms. > > ~v~~ Again, define "mechanics". 01oo
From: Tony Orlow on 17 Apr 2007 12:21 Lester Zick wrote: > On Fri, 13 Apr 2007 16:52:21 +0000 (UTC), stephen(a)nomail.com wrote: > >> In sci.math Tony Orlow <tony(a)lightlink.com> wrote: >>> Lester Zick wrote: >>>> On Mon, 2 Apr 2007 16:12:46 +0000 (UTC), stephen(a)nomail.com wrote: >>>> >>>>>> It is not true that the set of consecutive naturals starting at 1 with >>>>>> cardinality x has largest element x. A set of consecutive naturals >>>>>> starting at 1 need not have a largest element at all. >>>>> To be fair to Tony, he said "size", not "cardinality". If Tony wishes to define >>>>> "size" such that set of consecutive naturals starting at 1 with size x has a >>>>> largest element x, he can, but an immediate consequence of that definition >>>>> is that N does not have a size. >>>> Is that true? >>>> >>>> ~v~~ >>> Yes, Lester, Stephen is exactly right. I am very happy to see this >>> response. It follows from the assumptions. Axioms have merit, but >>> deserve periodic review. >>> 01oo >> Everything follows from the assumptions and definitions. > > And since definitions are considered neither true nor false everything > follows from raw assumptions which are considered neither true nor > false. > > ~v~~ Oh come on. Assumptions are considered true for the sake of the argument at hand. That's what an assumption IS. 01oo
From: Tony Orlow on 17 Apr 2007 12:51
Lester Zick wrote: > On Fri, 13 Apr 2007 13:42:06 -0400, Tony Orlow <tony(a)lightlink.com> > wrote: > >> 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. > > Or let's see you put something together that you can't take the > deriviative of and let's see how you managed to do it. > > ~v~~ Okay. What's the derivative of 0? 01oo |