# Operation (mathematics)

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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 ${\displaystyle \mathbb {R} \times \mathbb {R} }$ to ${\displaystyle \mathbb {R} }$.
In general, an operator + on a set A is a function of the form ${\displaystyle +:A^{k}\mapsto A}$. 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.