The term "discrete metric" refers to a mathematical concept often used in the study of topology. It describes a function that measures the distance between two points in such a way that the only possible distances are 0 or 1. In other words, it is a way of quantifying the distance between points in a way that is either fully inclusive or exclusive. Some possible synonyms for "discrete metric" include "binary metric," "Boolean metric," or "indivisible metric." Other related terms might include "pointwise metric," "piecewise metric," or "categorical metric." Ultimately, the appropriate synonym to use will depend on the specific context and intended meaning of the discussion at hand.