Lexical ordering also called lexicographic ordering, a method, given a finite ordered set of symbols, such as the letters of the alphabet, of ordering all finite sequences of those symbols. All finite sequences of letters, e.g., can be ordered as follows: first list all single letters in alphabetical order; then list all pairs of letters in the order aa, ab, . . . az; b. . . bz; . . . ; z. . . zz. Here pairs are first grouped and alphabetized according to the first letter of the pair, and then within these groups are alphabetized according to the second letter of the pair. All sequences of three letters, four letters, etc., are then listed in order by an analogous process. In this way every sequence of n letters, for any n, is listed. Lexical ordering differs from alphabetical ordering, although it makes use of it, because all sequences with n letters come before any sequence with n ! 1 letters; thus, zzt will come before aaab. One use of lexical ordering is to show that the set of all finite sequences of symbols, and thus the set of all words, is at most denumerably infinite. See also INFINIT. V.K.