Definition:Standard Discrete Metric

Definition
The 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 in the Kronecker delta notation as:
 * $d \left({x, y}\right) = \delta_{xy}$

The resulting metric space $M = \left({S, d}\right)$ is the discrete metric space on $S$.

This metric is also known as the standard discrete metric.

Also see

 * Discrete Metric is a Metric.

Linguistic Note
Be careful how you spell this. A common homophone horror is to refer to this as the discreet metric.

However, discreet means cautious or tactful, and describes somebody who is able to keep silent for political or delicate social reasons.