\begin{definition}[Definition:Ordinal/Definition 2]
Let $A$ be a set.
Then $A$ is an '''ordinal''' {{iff}} $A$ is:
: transitive
: epsilon-connected, that is:
:: $\forall x, y \in A: x \ne y \implies x \in y \lor y \in x$
: well-founded
\end{definition}