The discrete metric on a set is an example of a metric.

Definition[edit]

The discrete metric d on a set X is defined by

${\displaystyle d(x,x)=0,\,}$

${\displaystyle d(x,y)=1{\hbox{ if }}x\neq y.\,}$

Properties[edit]

• A discrete metric space is complete
• The topology induced by the discrete metric is the discrete topology, in which every set is open.