lexicographic order

English

Alternative forms

• lexicographical order

Noun

lexicographic order (plural lexicographic orders)

1. (mathematics) 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. (mathematics) Given sets (A₁, A₂, ..., A_n) and their total orderings (<₁, <₂, ..., <_n), the order <^d of A₁ × A₂ × ... × A_n such that (a₁, a₂, ..., a_n) <^d (b₁,b₂, ..., b_n) iff (∃m > 0) (∀ i < m) (a_i = b_i ) and (a_m <_m b_m )

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.