Definition:Chebyshev Distance

Definition
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 $x = \tuple {x_1, x_2}, y = \tuple {y_1, y_2} \in A_1 \times A_2$.

Real Number Plane
This metric is usually encountered in the context of the real number plane $\R^2$:

Also see

 * Chebyshev Distance is Metric


 * Definition:Taxicab Metric
 * Definition:$p$-Product Metric