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From: jsa@alexandria (Jon S Anthony)
Subject: Re: OO, C++, and something much better!
In-Reply-To: Alan Lovejoy's message of Fri, 14 Feb 1997 21:49:23 -0800
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Date: Sun, 16 Feb 1997 18:53:27 GMT
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In article <33054E63.C2A@concentric.net> Alan Lovejoy <alovejoy@concentric.net> writes:

> Is there a useful semantic distinction between "function" and "operator" 
> in math?  If so, what is it?

Generally speaking, the terms "operator" and "operation" are used to
refer to functions which map an "n-order" set to the "base" or
"1-order" set.  Let A be a set and A^n be the cross product of A with
it self n times (n could be 1).  If f is a function from A^n to A,
f:A^n -> A, then f is an "n-ary operation".  For example, addition is
a simple binary operation on N (set of naturals).  The identity
operation is a simple unary operation for any set.  Strictly speaking,
the term "operator" is used to refer to the particular symbol for the
operation, but in practice (outside a strictly formal account) this is
typically "slopped over".

/Jon
-- 
Jon Anthony
Organon Motives, Inc.
Belmont, MA 02178
617.484.3383
jsa@organon.com

