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This editable Main Article is under development and subject to a disclaimer.

[edit intro]

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

d ( x , x ) = 0 , {\displaystyle d(x,x)=0,\,}
d ( x , y ) = 1 if x ≠ y . {\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.