Definition:Standard Discrete Metric/Real Number Plane

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

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


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

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

where $x = \left({x_1, x_2}\right), y = \left({y_1, y_2}\right) \in \R^2$.

Also see

 * Standard Discrete Metric is Metric