A type of metric which satisfies a much stronger form of the triangle inequality: For all points x,y,z,
d(x,z) ≤ max(d(x,y),d(y,z))
Distances in an ultrametric "look like this":
,--y
/
x---<
\
`--z
rather than "like this":
_,-y
_,-' |
x< |
~ |
`-._ |
`-z
Examples include distances on a tree and the distance defined by the p-adic norm.