In order theory, a Hasse diagram (; German: ) is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction. Concretely, for a partially ordered set (S, =) one represents each element of S as a vertex in the plane and draws a line segment or curve that goes upward from x to y whenever y covers x (that is, whenever x < y and there is no z such that x < z < y). These curves may cross each other but must not touch any vertices other than their endpoints. Such a diagram, with labeled vertices, uniquely determines its partial order.