What are the exact meanings of the terms "operation", "function" and "map" (are they even exactly defined)? I have always believed that an "operation" was a map
$$S \times S \times [...] \times S \rightarrow S.$$
However, according to the always-so-reliable Wikipedia, an operation can be any map on the form
$$A_1 \times A_2 \times [...] \times A_3 \rightarrow S.$$
Fine, but Wolfram's MathWorld disagrees with Wikipedia and agrees with my original definition. Which is correct?
Also, above I've used the word "map" to describe operations. Is this correct use of the term? Could I have replaced "map" with "function" without changing any of the meaning, i.e., do "map" and "function" mean exactly the same thing, or is there a slight difference in formal meaning and/or customary meaning?