right|thumb|upright=1.15|Fig. 1 The Hasse diagram of the set of all subsets of a three-element set ordered by inclusion. Sets connected by an upward path, like and , are comparable, while e.g. and are not. In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The word partial is used to indicate that not every pair of elements needs to be comparable; that is, there may be pairs for which neither element precedes the other. Partial orders thus generalize total orders, in which every pair is comparable.
right|thumb|upright=115|fig 1 the hasse diagram of the set of all subsets of a three-element set ordered by inclusion sets connected by an upward path like and  are comparable while eg and are not in mathematics especially order theory a partial order on a set is an arrangement such that for certain pairs of elements one precedes the other the word partial is used to indicate that not every pair of elements needs to be comparable; that is there may be pairs for which neither element precedes the other partial orders thus generalize total orders in which every pair is comparable