Order (mathematics)

• Order of a finite set or algebraic structure [r]: The size, i.e., the number of elements, of a (possibly infinite) set. ^[e]
• Order (group theory) [r]: For a group, its cardinality; for an element of a group, the least positive integer (if one exists) such that raising the element to that power gives the identity. ^[e]
• Order (relation) [r]: An irreflexive antisymmetric transitive binary relation on a set. ^[e]
• Order (ring theory) [r]: A ring which is finitely generated as a Z-module. ^[e]

See also Order (disambiguation) for uses beyond mathematics.