Category:Definitions/Standard Discrete Metric

This category contains definitions related to Standard Discrete Metric.
Related results can be found in Category:Standard Discrete Metric.

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 $S$.