Discrete Metric

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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

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

${\displaystyle d(x,y)=1\text{ if }x\ne y.}$

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.