 If "M" is a metric space with metric "d", and "~" is an equivalence relation on "M", then we can endow the quotient set "M/~" with a pseudometric.Given two equivalence classes ["x"] and ["y"], we define

where the infimum is taken over all finite sequences formula_151 and formula_152 with formula_153, formula_154, formula_155.In general this will only define a pseudometric, i.e.