*109. A metric on M is an ultrametric if for all x, y, z = M we have d(x, z) max{d(x, y), d(y, z)}. (Intuitively this means that the trip from a to z cannot be broken into shorter legs by making a stopover at some y.) (a) Show that the ultrametric property implies the triangle inequality. (b) In an ultrametric space show that "all triangles are isosceles."