From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=-1.3 required=5.0 tests=BAYES_00,INVALID_MSGID autolearn=no autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 109fba,b87849933931bc93 X-Google-Attributes: gid109fba,public X-Google-Thread: 114809,b87849933931bc93 X-Google-Attributes: gid114809,public X-Google-Thread: 103376,b87849933931bc93 X-Google-Attributes: gid103376,public X-Google-Thread: 1108a1,b87849933931bc93 X-Google-Attributes: gid1108a1,public X-Google-Thread: fac41,b87849933931bc93 X-Google-Attributes: gidfac41,public From: jsa@alexandria (Jon S Anthony) Subject: Re: OO, C++, and something much better! Date: 1997/02/22 Message-ID: #1/1 X-Deja-AN: 220546079 Distribution: world References: <5de62l$f13$1@goanna.cs.rmit.edu.au> Organization: PSI Public Usenet Link Newsgroups: comp.lang.c++,comp.lang.smalltalk,comp.lang.eiffel,comp.lang.ada,comp.object Date: 1997-02-22T00:00:00+00:00 List-Id: In article piercarl@sabi.demon.co.uk (Piercarlo Grandi) writes: > >>> "jsa" == Jon S Anthony writes: > piercarl> beside. The common thing is not quite that they use > piercarl> non-alphabetic symbols, but that they don't use applicative > piercarl> syntax like 'f(....,....)'; > > jsa> ??? Mathematicians use the function "syntax" all the time. It's > jsa> probably one of the single _most_ used notations. > > I was writing of when they invent operator notation; when they design > operators, they often, but not always use non-alphabetic symbols, but > they usually use syntax (infix, postfix, prefix, ``around'', ...) that > is different from applicative syntax. What do you mean "often"? Where are you coming up with this stuff? The major problem you are having here is _exactly_ what Alan was getting at: You (for reasons that are beyond comprehension) seem to think that operators are defined by _syntax_. Well, in mathematics, THEY AREN'T! And until you get this straight you are going to continue to be confused. > piercarl> consider for examples of alphabetic operators commonly used in > piercarl> maths things like the 'lim' unary operator notation, > > jsa> How do you figure that "lim" is a unary operator??? > > Well, I distinguish it from non-operators because it does not involve > applicative syntax; it involves brief, ``special'' syntax, even if it > is not composed of special characters. I (and the rest of mathematics) don't _care_ about your _opinion_ here about why you think it's an operator. Syntax is IRRELEVANT! > As to ``unary'', well, this is arguable; one could argue that it is > a family of unary operators, actually, where: No, you can't argue that. In fact, it is hilarious to even suggest it. You're just wrong. This isn't _opinion_. And besides, since when is a "family of unary operators" a unary operator? > jsa> Depending on context it is a function of at least three arguments > jsa> (independent variable, the "limit", and a function) > > variable and limit ``specialize'' the operator ("unary operator This is ridiculous. Forget "specialize" or whatever. That's _not_ how it is defined. > or that it is really a ternary operator It's not a ternary operator either, because it is not an operator, because it is not taking a some A^n -> A. > If you want more obvious examples; just consider 'sin', which is often > written in operator notation: $y = sin x$, as well as function notation: > $y = sin(x)$. Same goes for "log", which is a unary operator, I would Well, at least here you really have a couple of operators. > jsa> and may well a) not even have a value and b) even if it does, it > jsa> may not be in the range of the function argument. Actually, in > jsa> mathematical parlence "lim" is not even an operator. > > Of course it is -- if one looks at how it is written in most textbooks, > 'lim' does not look like a function application. Now, my argument is Will you get a clue??? No. It is not an operator. Syntax is irrelevant to this determination. What makes you think for even a fempto second that just because _you_ think "operation" in mathematics should be defined by "syntax" mathematicians should change the _actual_ definition, toss out a century or so of practice, etc??? You really can't be serious. This is absolutely laughable! It's actually a whole set of functions (one for each limit) Let F = Set of functions on R let S = R union {"undefined", oo, -oo} let a = limit point lim-a: FxRx{a} -> S > but what is an operator *symbol*, WHO CARES!!! > usually evident by visual inspection. Let me insist: this usually You can insist alll you want. Doesn't mean a damn thing. /Jon -- Jon Anthony Organon Motives, Inc. Belmont, MA 02178 617.484.3383 jsa@organon.com