\begin{definition}[Definition:P-Product Metric/Real Number Plane]
Let $\R^2$ be the real number plane.
Let $p \in \R_{\ge 1}$.
The '''$p$-product metric''' on $\R^2$ is defined as:
:$\ds \map {d_p} {x, y} := \sqrt [p] {\size {x_1 - y_1}^p + \size {x_2 - y_2}^p}$
where $x = \tuple {x_1, x_2}, y = \tuple {y_1, y_2} \in \R^2$.
\end{definition}