Definition:Standard Discrete Metric/Real Number Plane

Definition
Let $\R^2$ be the real number plane.

The (standard) discrete metric on $\R^2$ is defined as:


 * $\map {d_0} {x, y} := \begin {cases}

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

where $x = \tuple {x_1, x_2}, y = \tuple {y_1, y_2} \in \R^2$.

Also see

 * Standard Discrete Metric is Metric