Metric space
A metric space is a pair, 
of a set 
and a metric 
. The metric 
represents a distance function between pairs of points of which has the following properties:
- Symmetry (
) - Non-negativity (
- Uniqueness (
if and only if 
) - Triangle Inequality (
for all points 
).
)
if and only if 
)
for all points 
).Intuitively, a metric space is a generalization of the distance between two objects (where "objects" can be anything, including points, functions, graphics, or grades). The above properties follow from our notion of distance. Non-negativity stems from the idea that A cannot be closer to B than B is to itself; Uniqueness results from two objects being identical if and only if they are the same object; and the Triangle Inequality corresponds to the idea that a direct path between points A and B should be at least as short as a roundabout path that visits some point C first.
Popular metrics
- The Euclidean Metric on
, with the "usual" meaning of distance
, with the "usual" meaning of distance- The Discrete Metric on any set
This article is a stub. Help us out by expanding it.
