product set | set direct product

The Cartesian product of two sets A and B (also called the product set, set direct product, or cross product) is defined to be the set of all points (a, b) where a element A and b element B. It is denoted A×B, and is called the Cartesian product since it originated in Descartes' formulation of analytic geometry. In the Cartesian view, points in the plane are specified by their vertical and horizontal coordinates, with points on a line being specified by just one coordinate. The main examples of direct products are Euclidean three-space (R×R×R, where R are the real numbers), and the plane (R×R). The graph product is sometimes called the Cartesian product (Vizing 1963, Clark and Suen 2000).

direct product | disjoint union | external direct product | external direct sum | graph Cartesian product | graph product | group direct product | product space