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

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $2$: Continuity generalized: metric spaces: $2.2$: Examples: Examples $2.2.3$