A binary operation is an operation with arity two, involving two operands.

A binary operation on a set is a function that maps elements of the Cartesian product: ## Examples

In the set of real numbers, and in any field for that matter:

• Addition ( );
• Subtraction ( );
• Multiplication ( );
• While not a binary operation in the strictest sense, as division by zero is undefined, division ( ) is commonly thought of as an operation.

## Notation

Because a binary operation on a set is also a function from to , and therefore a relation and a subset of the cartesian product , the following notations are valid:

• , when viewing as a set;
• , when viewing as a relation;
• , when viewing as a function;

However, we will adopt the preferred notation as an alternative to the function notation . One should not confuse this preferred notation to the relation notation; the preferred notation for binary operations is an expression for a value in the codomain, while the relation notation is an expression of a statement.