Definition: Lexicographic order and comparison

Lexicographic ordering means dictionary like ordering on types that have several elements in some defined sequence.

If the first element of a sequence A is less than the first element of a sequence B then A is lexicographically less than B. Likewise, if the first element of A is greater than the first element of B then A is lexicographically greater than B. If the first element of A is equal to the first element of B then the lexicographic order of A and B is determined by the lexicographic order of A's sequence and B's sequence with the first element removed from both sequences. An empty sequence is smaller than a non-empty sequence.

The lexicographic order is commonly used for strings, vector, matrix and color classes.