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lexicographic order



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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, ..., 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 )

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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.