Definition:Lexicographic Order

Definition
Let $\left({S_1, \preceq_1}\right)$ and $\left({S_2, \preceq_2}\right)$ be ordered sets.

The lexicographic order on $S_1 \times S_2$ is the relation $\preccurlyeq$ defined on $S_1 \times S_2$ as:
 * $\left({x_1, x_2}\right) \preccurlyeq \left({y_1, y_2}\right) \iff \left({x_1 \prec_1 y_1}\right) \lor \left({x_1 = y_1 \land x_2 \preceq_2 y_2}\right)$

Also known as
Lexicographic order can also be known as the more unwieldy lexicographical ordering.

Also see

 * Lexicographic Order is Ordering