Definition:Chebyshev Distance/Real Vector Space

Definition
Let $\R^n$ be an $n$-dimensional real vector space.

The Chebyshev distance on $\R^n$ is defined as:


 * $\displaystyle d_\infty \left({x, y}\right):= \max_{i \mathop = 1}^n {\left\vert{x_i - y_i}\right\vert}$

where $x = \left({x_1, x_2, \ldots, x_n}\right), y = \left({y_1, y_2, \ldots, y_n}\right) \in \R^n$.

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

Also see

 * Chebyshev Distance on Real Vector Space is Metric