Definition:Standard Discrete Metric

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


 * $d \left({x, y}\right) = \begin{cases}

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

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

The resulting metric space $M = \left({S, d}\right)$ 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 Topological Space