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In mathematics, the lexicographic or lexicographical order (also known as lexical order, dictionary order, alphabetical order or lexicographic(al) product) is a generalization of the way the alphabetical order of words is based on the alphabetical order of their component letters. ==Definition== Given two partially ordered sets ''A'' and ''B'', the lexicographical order on the Cartesian product ''A'' × ''B'' is defined as :(''a'',''b'') ≤ (''a''′,''b''′) if and only if ''a'' < ''a''′ or (''a'' = ''a''′ and ''b'' ≤ ''b''′). The result is a partial order. If ''A'' and ''B'' are each totally ordered, then the result is a total order as well. The lexicographical order of two totally ordered sets is thus a linear extension of their product order. More generally, one can define the lexicographic order on the Cartesian product of ''n'' ordered sets, on the Cartesian product of a countably infinite family of ordered sets, and on the union of such sets. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lexicographical order」の詳細全文を読む スポンサード リンク
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