or lexicographic order,n. the arrangement of a set of items in accordance with a recursive algorithm, such as the entries in a dictionary, whose order depends on their first letter unless those are identical, in which case it is the second that decides, and so on. The reverse-lexical order orders by last letters; this is particularly useful for ordering finite words constructed from an infinite alphabet, as in an infinite-dimensional vector space. When polynomials are ordered in this way, a polynomial is greater than zero if its highest order term has a positive coefficient, and the order is a total ordering.