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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 set A is related to set B if A is a subset of B. Another common example is the divisibility relation on the set of positive integers, where integer a is related to integer b if a divides b. Graph theory also provides examples, such as the relation between vertices in a directed acyclic graph where there is a path from one vertex to another. Visual representations of partial orders are often depicted using Hasse diagrams, which omit reflexive and transitive edges and draw comparable elements with an upward line.