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":

rather than "like this":
  _,-'   |
x<       |
  ~      |
   `-._  |

Examples include distances on a tree and the distance defined by the p-adic norm.

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