Category:Discrete Metrics

This category contains results about Discrete Metrics.

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 $S$.