Question: When can a distance function d(x,y) be called metric, pseudo-metric, quasi-metric or semi-metric?
| Constraint | Metric | Pseudo | Quasi | Semi |
|---|---|---|---|---|
| Non-negativity: d(x,y) ≥ 0 | x | x | x | x |
| Identity of indiscernibles: d(x,y)=0 ⇒ x=y | x | x | x | |
| Symmetry: d(x,y) = d(y,x) | x | x | x | |
| Triangle inequality: d(x,z) ≤ d(x,y)+d(y,z) | x | x | x |
Table derived from Wikipedia article on metric spaces: http://en.wikipedia.org/wiki/Metric_(mathematics)
Leave a Reply
You must be logged in to post a comment.