lexicographic order

Noun

 * 1)  Formally, given two partially ordered sets A and B, the order ≤ on the Cartesian product A × B such that (a,b) ≤ (a′,b′) if and only if a < a′ or (a = a′ and b ≤ b′).
 * 2)  Given sets (A1, A2, ..., An) and their total orderings (<1, <2, ...,  0) (∀ i < m) (ai = bi ) and (am <m bm )

Usage notes
More generally, one can define the lexicographic order (a) on the Cartesian product of n ordered sets, (b) on the Cartesian product of a countably infinite family of ordered sets, and (c) on the union of such sets.