Operation (mathematics)

In mathematics, an operator is usually defined as a function which maps some finite Cartesian power of a set to itself. For instance, the real numbers form a set, and addition is a function mapping $\mathbb {R} \times \mathbb {R}$ to $\mathbb {R}$.

In general, an operator + on a set A is a function of the form $+:A^{k}\mapsto A$. We say that + is a k-ary operator, indicating the number of arguments it takes. In the case of real number addition, the operator is binary because it takes two arguments.