Discrete metric: Difference between revisions

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

The discrete metric d on a set X is defined by

d(x,x)=0,\,

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

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

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	The '''discrete metric''' on a set is an example of a [[metric]].		The '''discrete metric''' on a set is an example of a [[metric]].