Definition:Cartesian Product/Cartesian Space/Three Dimensions

Definition
Let $S$ be a set. The cartesian $3$rd power of $S$ is:


 * $S^3 = S \times S \times S = \set {\tuple {x_1, x_2, x_3}: x_1, x_2, x_3 \in S}$

The set $S^3$ called a cartesian space of $3$ dimensions.

Cartesian 3-Space
When $S$ is the set of real numbers $\R$, the cartesian product takes on a special significance.

Also see

 * Definition:Cartesian Plane