n. a relation that is reflexive, transitive, and symmetric; it imposes a partition on its domain of definition, so that two elements belong to the same subset if and only if the relation holds be tween them. For example, since two integers are congruent modulo n if and only if their difference is divisible by n, congruence mod n is reflexive (a ≡ a for all a), transitive (if a ≡ b and b ≡ c, then a ≡ c), and symmetric (a ≡ b if and only if b ≡ a), so that this is an equivalence relation; hence it can be proved that , since every integer has a unique smallest positive remainder when divided by n, and so is congruent mod n to only one of the integers between 1 and n, these congruence classes are both disjoint and exhaustive of all the integers, and so constitute a partition of them.