- 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.
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.