The Definition of Points
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From: Lester Zick on 16 Apr 2007 13:52 On Mon, 16 Apr 2007 01:03:22 +0100, Alan Smaill <smaill(a)SPAMinf.ed.ac.uk> wrote: >Lester Zick <dontbother(a)nowhere.net> writes: > >> On Sun, 15 Apr 2007 21:34:09 +0100, Alan Smaill >> <smaill(a)SPAMinf.ed.ac.uk> wrote: >> >>>>>>>>>>>Dear me ... L'Hospital's rule is invalid. >>>> >>>> So returning to the original point, would you care to explain your >>>> claim that L'Hospital's rule is invalid? >>> >>>haha! >> >> Why am I not surprized? Remarkable how many mathematiker opinions on >> the subject of mathematics don't quite hold up to critical scrutiny. > >knew you wouldn't get it, >irony is not a strong point with Ziko. I'll grant you I'm much more adept at hyperbolic rhetorical irony than simplistic irony which tends to go right past me much as mathematitcs tends to go right past you. >nor indeed do you bother defending your own view that you can use >Hospital to work out the value for 0/0. I never claimed L'Hospital's rule was valid. I assume its validity or at least its utility was established by L'Hospital much as I assume the validity or at least the uitility of 1+1=2 has been established by others just as I assume you're a mathematiker because you're too lazy or stupid to demonstrate the truth of your arguments but not too lazy or stupid to formulate arguments whose truth you can't demonstrate. >well, there you go. Yes indeedy do, Snail. ~v~~
From: MoeBlee on 16 Apr 2007 15:17 On Apr 14, 7:08 pm, Tony Orlow <t...(a)lightlink.com> wrote: > Maybe I don't understand Robinson as well as I should, but it seems to > me the basis of his analysis was semantic, regarding statements that > would be considered true of *N if true of N. But, do go on... "But do go on..." Hey, smartass, YOU'RE the one who waves non-standard analysis like banner when you don't know ANYTIHNG about it. If you want to know anything about non-standard analysis, then you'd start by learning basic predicate calculus, set theory, and mathematical logic (personally, I'd recommend that order). > > The MAJOR point - the hypothetical nature of mathematical reasoning > > (think about the word 'if' twice in the poster's paragraph) and the > > inessentiality of what words we use to name mathematical objects and > > their properties. > > I guess, by "inessentiality", you mean any attribute that one could > assign to any object... IF that's what you mean, or not.... No, smartass, months ago, several times, I explained in detail to you, and with respect to the technicalities, what I mean. > > I've been trying to get you to understand that for about two years > > now. > > Perhaps what you mean is exactly what I am trying to get across to > Lester. If the truth table is the same, then it's the same logical > function. It doesn't matter what the parameters are, it always works the > same way. The pattern defines the relationship. That's getting closer. I won't quibble with it. But I'll just say that in mathematical logic we have even more precise ways of saying it. > On the subject of ifs, "if this then that" means logical implication, or > causality, and sometimes it's hard to tell which is meant, or if they're > being confused. Is that what you "mean"? No. > >> I don't take transfinite cardinality to mean > >> "size". You say I missed the point. You didn't intersect the line. > > > You just did it AGAIN. We and the poster to whom you responded KNOW > > that you don't take cardinality as capturing your notion of size. The > > point is then just for your to recognize that IF by 'size' we mean > > cardinality, then certain sentences follow and certain sentences don't > > follow and that what is important is not whether we use 'size' or > > 'cardinality' or whatever word but rather the mathematical relations > > that are studied even if we were to use the words 'schmize' or > > 'shmardinal' or whatever. THAT, to which you did not respond, is, at least at this informal level of discussion with you, good enough for a start as to what I mean. MoeBlee
From: Alan Smaill on 16 Apr 2007 15:40 Lester Zick <dontbother(a)nowhere.net> writes: > On Mon, 16 Apr 2007 01:03:22 +0100, Alan Smaill > <smaill(a)SPAMinf.ed.ac.uk> wrote: > >>knew you wouldn't get it, >>irony is not a strong point with Ziko. > > I'll grant you I'm much more adept at hyperbolic rhetorical irony than > simplistic irony which tends to go right past me much as mathematitcs > tends to go right past you. self-ascription of abilities is another Ziko trait; some improvement on the irony level her, thuogh ... >>nor indeed do you bother defending your own view that you can use >>Hospital to work out the value for 0/0. > > I never claimed L'Hospital's rule was valid. I assume its validity tsk tsk > or > at least its utility was established by L'Hospital much as I assume > the validity or at least the uitility of 1+1=2 has been established by > others just as I assume you're a mathematiker because you're too lazy > or stupid to demonstrate the truth of your arguments but not too lazy > or stupid to formulate arguments whose truth you can't demonstrate. clearly; your failure to explain why l'Hospital might be applicable to work out a value for 0/0 is equally clear. >>well, there you go. > > Yes indeedy do, Snail. indeedy indeed. > ~v~~ -- Alan Smaill
From: Lester Zick on 16 Apr 2007 19:49 On Mon, 16 Apr 2007 20:40:45 +0100, Alan Smaill <smaill(a)SPAMinf.ed.ac.uk> wrote: >Lester Zick <dontbother(a)nowhere.net> writes: > >> On Mon, 16 Apr 2007 01:03:22 +0100, Alan Smaill >> <smaill(a)SPAMinf.ed.ac.uk> wrote: >> >>>knew you wouldn't get it, >>>irony is not a strong point with Ziko. >> >> I'll grant you I'm much more adept at hyperbolic rhetorical irony than >> simplistic irony which tends to go right past me much as mathematitcs >> tends to go right past you. > >self-ascription of abilities is another Ziko trait; >some improvement on the irony level her, thuogh ... If not exactly on the spelling level. ~v~~
From: Ilmari Karonen on 17 Apr 2007 04:38
K_h <KHolmes(a)SX729.com> kirjoitti 16.04.2007: > > You seem to be saying that, for totally ordered sets, equality only exists > in the case of identity and therefore equality among two distinct members > cannot be defined in the order. If that is the case then what you are > saying is correct. So what I would like is an authoritative source that > says that. Both Wolfram and Wikipedia do not say that. If they did then > the definition would say something like "...for any distinct members x y, > x<y or y<x" and there wouldn't be statements like "...for any x and y, x<y > or y<x or y=x". In my experience, many if not most treatments of the subject seem to reserve "=" specifically for identity, using some other symbol (often "~") for equivalence. For hypertext sources such as MathWorld or Wikipedia this may be hard to ascertain, since such definitions aren't (and, practically, cannot be) repeated on every page, and, at least for Wikipedia, there probably is no convenient central list of symbol definitions, but for books (including more traditionally structured online sources) I'd expect a definition to be given somewhere. > I am totally prepared to admit that your understanding is correct and both > Wolfram and Wikipedia are badly worded. There is lots of misinformation on > the internet. What troubles me is that the books on set theory I have also > have their definitions worded like wolfram and Wikipedia. I'd suggest you check those books to see how they define "=". If they don't define it at all, I'd put my money on the intended meaning being identity. -- Ilmari Karonen To reply by e-mail, please replace ".invalid" with ".net" in address. |