Definition:Lexicographic Order/Ordinals

Definition
The lexicographic order is a relation on ordered pairs of ordinals denoted $\preccurlyeq_l$.

$\preccurlyeq_l$ is the set of all ordered pairs $\tuple {\tuple {\alpha, \beta}, \tuple {\gamma, \delta} }$ such that:


 * $(1): \quad$ Each $\alpha, \beta, \gamma, \delta$ is a member of the class of all ordinals
 * $(2): \quad$ $\alpha \in \gamma$ or $\alpha = \gamma \land \beta \in \delta$

Also see

 * Definition:Canonical Order