Definition:Standard Discrete Metric

Definition
The standard discrete metric on a set $S$ is the metric satisfying:


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

0 & : x = y \\ 1 & : x \ne y \end{cases}$

This can be expressed using the Kronecker delta notation as:
 * $\map d {x, y} = 1 - \delta_{x y}$

The resulting metric space $M = \struct {S, d}$ is the standard discrete metric space on $S$.

Also known as
This metric is also reported in some texts as the discrete metric.

Also see

 * Standard Discrete Metric is Metric
 * Definition:Discrete Space