Definition:Standard Discrete Metric/Real Number Plane

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

The discrete metric on $\R^n$ is defined as:


 * $\displaystyle d_0 \left({x, y}\right) := \begin{cases}

0 & : x = y \\ 1 & : \exists i \in \left\{{1, 2, \ldots, n}\right\}: x_i \ne y_i \end{cases}$

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

Also see

 * Standard Discrete Metric is Metric