In mathematics, a binary operation on a set is a function of two variables which assigns a value to any pair of elements of the set: principal motivating examples include the arithmetic and elementary algebraic operations of addition, subtraction, multiplication and division.
Formally, a binary operation on a set S is a function on the Cartesian product
- given by
using operator notation rather than functional notation, which would call for writing .
A binary operation may satisfy further conditions.
Special elements which may be associated with a binary operation include: