lexicographic order

English

Alternative forms

lexicographical order

Noun

lexicographic order (plural lexicographic orders)

(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′).
(mathematics) Given sets (A₁, A₂, ..., A_n) and their total orderings (<₁, <₂, ..., <_n), the order <^d of A₁ × A₂ × ... × A_n such that (a₁, a₂, ..., a_n) <^d (b₁,b₂, ..., b_n) iff (∃m > 0) (∀ i < m) (a_i = b_i ) and (a_m <_m b_m )

Usage notes

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.

单词	lexicographic order
释义	lexicographic order English Alternative forms lexicographical order Noun lexicographic order (plural lexicographic orders) (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′). (mathematics) Given sets (A₁, A₂, ..., A_n) and their total orderings (<₁, <₂, ..., <_n), the order <^d of A₁ × A₂ × ... × A_n such that (a₁, a₂, ..., a_n) <^d (b₁,b₂, ..., b_n) iff (∃m > 0) (∀ i < m) (a_i = b_i ) and (a_m <_m b_m ) Usage notes 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.
随便看	obsonantor obsonantur obsonarant obsonaras obsonarat obsonaratis obsonare obsonarem obsonaremini obsonaremur obsonaremus obsonarent obsonarentur obsonarer obsonarere obsonareris obsonares obsonaret obsonaretis obsonaretur obsonari obsonarim obsonarimus obsonarint obsonaris