Lexicographic-order Definition

(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′).

(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)