Definition:Cartesian Product/Cartesian Space/Two Dimensions

Definition
Let $S$ be a set. The cartesian $2$nd power of $S$ is:


 * $\displaystyle S^2 = S \times S = \set {\tuple {x_1, x_2}: x_1, x_2 \in S}$

Thus $S^2 = S \times S$

The set $S^2$ called a cartesian space of $2$ dimensions.

Cartesian Plane
When $S$ is the set of real numbers $\R$, the cartesian product takes on a special significance.