\begin{definition}[Definition:Cartesian Product/Cartesian Space/Three Dimensions]
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'''.
\end{definition}