lexicographic order

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′).

Given sets (A₁, A₂, ..., Aₙ) and their total orderings (<₁, <₂, ..., <ₙ), the order <ᵈ of A₁ × A₂ × ... × Aₙ such that (a₁, a₂, ..., aₙ) <ᵈ (b₁,b₂, ..., bₙ) iff (∃m > 0) (∀ i < m) (aᵢ = bᵢ ) and (aₘ <ₘ bₘ )