Order Definition(Partial order A partial order is a set S with a binary relation on S, which is transitive and irreflexive Definition(Linear order) a partial order is a linear order. if it satisfies the trichotomy law:. <y or a=y or y<.. Definition(Well ordering) A linear order is well ordered if every nonempty set A of s has a least elementOrder . Definition (Partial order) . . A partial order is a set S with a binary relation < on S, which is transitive and irreflexive. . Definition (Linear order) . . A partial order < is a linear order, if it satisfies the trichotomy law: x < y or x = y or y < x. . Definition (Well ordering) . . A linear order is well ordered if every nonempty set A of S has a least element. Yi Li (Fudan University) Discrete Mathematics March 12, 2013 9 / 20