\begin{definition}[Definition:Chebyshev Distance/Real Number Plane]
Let $\R^2$ be the real number plane.
The '''Chebyshev distance''' on $\R^2$ is defined as:
:$\map {d_\infty} {x, y}:= \max \set {\size {x_1 - y_1}, \size {x_2 - y_2} }$
where $x = \tuple {x_1, x_2}, y = \tuple {y_1, y_2} \in \R^2$.
\end{definition}