Metric (analysis)
From AoPSWiki
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 
.
Together, the set and the metric form a metric space.
Common metrics
- For
, the Euclidean metric 
is the conventional distance function.
- For any set , the discrete metric
and 
otherwise.
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