# Metric

### From Glossary

A nonnegative, real-valued function, , on pairs from a set such that for each and in

The function is also called a *distance*; the pair is a
*metric space*. Condition (3) is called the Triangle inequality.
A space is *metrizable* if a metric can be
defined. A metric is induced by a norm if one exists:
See Hausdorff metric.