\begin{definition}[Definition:Cartesian Product/Cartesian Space/Two Dimensions]
Let $S$ be a set.
The '''cartesian $2$nd power of $S$''' is:
:$S^2 = S \times S = \set {\tuple {x_1, x_2}: x_1, x_2 \in S}$
The set $S^2$ called a '''cartesian space of $2$ dimensions'''.
\end{definition}