Definition:Lexicographic Order

Definition
Let $\struct {S_1, \preceq_1}$ and $\struct {S_2, \preceq_2}$ be ordered sets.

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

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

Some sources refer to it as dictionary order.

Also see

 * Lexicographic Order is Ordering
 * Definition:Colexicographic Order