Re: c.d.theory glossary -- definition of "class"

"x" <x-false_at_yahoo.com> wrote in message news:40e06675_at_post.usenet.com...
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> "Paul" <paul_at_test.com> wrote in message
> news:QeZDc.448$Fc7.116786_at_stones.force9.net...
> > Marshall Spight wrote:
> > > I am in general agreement. But perhaps you can clarify something
> > > for me: how is an operator different from a function?
> > >
> > > ISTM that "function" is the term with the clearest definition
> > > and the longest history. I tend to use "function" and "operator"
> > > interchangably, but I can't help but have this nagging feeling
> > > that there is some nuance to the second term that I'm unaware
> > > of.
> >
> > There's some discussion of this here:
> > http://en.wikipedia.org/wiki/Operator
> >
> > Basically it seems to be saying an operator is a function bundled with
> > the types of its operands. I'm still don't entirely understand the
> > distinction though. Maybe for a function you just specify the *set* of
> > the operands rather than the *type*?
> >
> > It says that "Functions can therefore conversely be considered
> > operators, for which we forget some of the type baggage, leaving just
> > labels for the domain and codomain". I'm not sure what it means by
> > "labels" here.
> >
> > Though further on it seems to say they mean the same thing and the word
> > "operator" is just used by convention for things like functions that
> > have functions as operands, or functions that have matrices as operands.
>
> It seems the term function is used in Calculus and the term operator is
used
> in Algebra.

At least informally, I think of operators as being binary functions so that it can be written as

a operator b which would be equivalent to f(a,b)

Then if you have a bunch of operators, there is an implied ordering so that only two are addressed at one time and a + b - c * d could mean +(a,-(b,*(c,d))) with each operator acting on two inputs.

So, this might not be the formal distinction, but I think of operators and functions as having different notation and not different meaning and of operators at least casually limited to binary (perhaps unary) functions. Formally I'm just fine with considering them the same thing and prefer using the term Function so that I don't limit it in my mind to binary operators.

--dawn Received on Wed Jun 30 2004 - 01:26:34 CEST