Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the lexicographic or lexicographical order, (also known as dictionary order, alphabetic order or lexicographic(al) product), is a natural order structure of the Cartesian product of two ordered sets. Given two partially ordered sets A and B, the lexicographical order on the Cartesian product A x 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 totally ordered, then the result is a total order also. 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.

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