Metric (analysis)
Revision as of 08:26, 8 August 2009 by JBL (talk | contribs) (moved Metric (set theory) to Metric (analysis): Set theory? Gimme a break ... (though if someone thought "topology" was better than "analysis," I wouldn't mind))
A metric 
on a set 
is a function 
which obeys the following three properties:
- Symmetry:
for all points 
. - Positivity:
for all and 
if and only if 
. - The triangle inequality:
for all 
.
for all points 
.
for all 
if and only if 
.
for all 
.Together, the set and the metric form a metric space.
Common metrics
- For
, the Euclidean metric 
is the conventional distance function.
, the 
is the - For any set
, the discrete metric 
and 
otherwise.
and 
otherwise.
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