
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 (A_{1}, A_{2}, ..., A_{n}) and their total orderings (<_{1}, <_{2}, ..., <_{n}), the order <^{d} of A_{1} × A_{2} × ... × A_{n} such that (a_{1}, a_{2}, ..., a_{n}) <^{d} (b_{1},b_{2}, ..., b_{n}) iff (?m > 0) (? i < m) (a_{i} = b_{i} ) and (a_{m} <_{m} b_{m} ) ¹
¹ Source: wiktionary.com
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