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Direct Product (Set)

The direct product of two sets $A$ and $B$ is defined to be the set of all points $(a,b)$ where $a\in A$ and $b\in B$. The direct product is denoted $A\times B$ or $A\otimes B$ and is also 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 3-space ( $\Bbb{R}\otimes\Bbb{R}\otimes\Bbb{R}$, where $\Bbb{R}$ are the Real Numbers), and the plane ( $\Bbb{R}\times\Bbb{R}$).

© 1996-9 Eric W. Weisstein