apartness relation

An apartness relation is a binary relation that, instead of saying when two things are the same (as an equivalence relation), states when two things are different – an inequality relation. Apartness relations are most used in constructive mathematics; in classical mathematics, equivalence relations can take their place (mediated by negation). The apartness relations that we discuss here are sometimes called point–point apartness, to distinguish this from the related concepts of set–set or...