Binary Operator

A binary operator in mathematics is defined as an operator defined on a set that takes two elements of the set and returns a single element. An example would be integer multiplication "*" where a,b are both integers and a*b returns an integer.

Does it have to return an element of the same set?

No. Division is a good example: division of two integers may yield a fraction (which is obviously not of the set of integers). This does not keep division from being an operator; it merely means that the set of integers is not closed over division.

What do you call an operator that takes one argument and returns two elements? e.g.: SQRT(4) -> {-2, 2}?

That would be "unary" because of the number of arguments it takes. I don't know if there are different names according to the number of elements returned.

CategoryMath