orderreversing
Order-reversing, or antitone, describes a function between partially ordered sets that inverts the order. Formally, a function f: (P, ≤P) → (Q, ≤Q) is order-reversing if for all x, y in P, x ≤P y implies f(x) ≥Q f(y). Equivalently, f is order-preserving when viewed as a map from P to the dual poset Q^op, where the order relation is reversed.
Key properties include how order-reversing maps compose. The composition of two order-reversing maps is order-preserving. The
Examples help anchor the concept. On the real numbers with the usual ≤, the negation map f(x) =