Definition of Lexicographic order

1. Noun. (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?). ¹



2. Noun. (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 ) ¹

¹ Source: wiktionary.com

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