\begin{definition}[Definition:Chebyshev Distance]
Let $M_1 = \struct {A_1, d_1}$ and $M_2 = \struct {A_2, d_2}$ be metric spaces.
Let $A_1 \times A_2$ be the cartesian product of $A_1$ and $A_2$.
The '''Chebyshev distance''' on $A_1 \times A_2$ is defined as:
:$\map {d_\infty} {x, y} := \max \set {\map {d_1} {x_1, y_1}, \map {d_2} {x_2, y_2} }$
where $x = \tuple {x_1, x_2}, y = \tuple {y_1, y_2} \in A_1 \times A_2$.
\end{definition}