Ultrametrics
An ultrametric is a metric d defined on a set X that satisfies the ultrametric inequality: for all x, y, z in X, d(x, z) ≤ max{ d(x, y), d(y, z) }. This strong form of the triangle inequality implies several distinctive geometric and topological features.
One consequence is that every triangle in an ultrametric space is isosceles with the two largest sides
Examples and constructions: the canonical example comes from p-adic numbers. The p-adic metric d_p(x, y) := p^{-v_p(x
Applications and relevance: ultrametrics underpin models in biology (phylogenetics), linguistics, and information science. They are used