Section 6.1
Binary operations

The map that takes an element of Z to its negative is a unary operation on Z, while addition and multiplication are binary operations on Z in the following sense.

Definition

Let V be a set.

A unary operation is a map V -> V.

A binary operation is a map V × V -> V.


For a binary operation * : V -> V we often use infix notation:

a * b = *(a,b).

This is in accordance with the familiar notation for addition + and multiplication · in, for example, C.

A set together with a number of operations defined on it is called a structure.