Cartesian Product

If $X$ and $Y$ are sets, then we define the Cartesian Product $X \times Y$ to be the collection of ordered pairs, e.g. $(x, y)$, whose first component lies in $X$ and whose second component lies in $Y$

$X \times Y = \{(x, y) | x \in X, y \in Y\}$

An example would be $\mathbb{R} \times \mathbb{R} = \mathbb{R}^{2}$ (i.e. the cartesian plane). $\mathbb{R}^{2}$ is the cartesian product of “crossing” $\mathbb{R}$ with itself.