Definition:Lexicographic Order/Ordinals

Definition
The lexicographic order is a relation on ordered pairs of ordinals denoted $\operatorname{Le}$.

$\operatorname{Le}$ is the set of all ordered pairs $\left({\left({\alpha, \beta}\right), \left({\gamma, \delta}\right)}\right)$ such that:


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

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

Also see

 * Definition:Canonical Order