A binary operation f(x, y) is an operation that applies to two quantities or expressions x and y. A binary operation on a nonempty set A is a map f:A×A->A such that 1.f is defined for every pair of elements in A, and 2.f uniquely associates each pair of elements in A to some element of A. Examples of binary operation on A from A×A to A include addition (+), subtraction (-), multiplication (×) and division (÷).

binary operator