lexicographic order

noun

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′).

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Meanings

nounlexicographic order (plural lexicographic orders)

plural lexicographic orders · alternative lexicographical order

  1. mathematicsFormally, 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. mathematicsGiven 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 )
Cite this entry
APA

lexicographic order. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/lexicographic%20order

MLA

“lexicographic order.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/lexicographic%20order. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “lexicographic order,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/lexicographic%20order.

Source: lexicographic order on Wiktionary, CC BY-SA 4.0.