A metric space
which associates to each pair
Further more, the metric must satisfy the following properties:
- For any
, we have - (Positivity) For any distinct
, we have - (Symmetry) For any
, we have - (triangle inequality) For any
, we have
Example: Euclidean Space
, the Euclidean space of dimension, use Euclidean distance as the metric.
Example: Taxicab Space
Example: Sup norm metric
space see also: p-norm
The above
, , and metric spaces are special case of the metrics, where