Cartesian product

In mathematics, sets can be used to make new sets. Suppose we have two sets A and B. Then the Cartesian product of A with B is written as A × B and is the set of all ordered pairs whose first element is a member of A and whose second element is a member of B.

For example, let A = {1, 2, 3} and B = {a, b}. Then:

[math]\displaystyle{ A \times B = \{(1, a), (1, b), (2, a), (2, b), (3, a), (3, b)\} }[/math]