osittaisjärjestyksestä
Partial order refers to a binary relation on a set that is reflexive, antisymmetric, and transitive. A relation < is a partial order if for any elements a, b, and c in the set: 1. a < a (reflexivity) 2. If a < b and b < a, then a = b (antisymmetry) 3. If a < b and b < c, then a < c (transitivity). Unlike a total order, a partial order does not require that every pair of elements be comparable. This means there can exist elements x and y in the set such that neither x < y nor y < x holds. When such a pair exists, x and y are considered incomparable. The set together with the partial order relation is called a partially ordered set, often denoted as (S, <).
Examples of partial orders include the subset relation on the power set of a given set, where