Definition:Ordinal/Definition 2

Definition
Let $A$ be a set.

Then $A$ is an ordinal $A$ is:


 * transitive


 * epsilon-connected, that is:
 * $\forall x, y \in A: x \ne y \implies x \in y \lor y \in x$


 * well-founded

Also see

 * Equivalence of Definitions of Ordinal