Chebyshev Distance on Real Vector Space is Metric

Theorem
The Chebyshev distance on $\R^n$:


 * $\ds \forall x, y \in \R^n: \map {d_\infty} {x, y}:= \max_{i \mathop = 1}^n {\size {x_i - y_i} }$

is a metric.