Definition:Strict Well-Ordering/Definition 2

Definition
Let $A$ be a set or class.

Let $\prec$ be a relation on $A$.

Then $\prec$ is a strict well-ordering of $A$ :


 * $\prec$ connects $A$
 * $\prec$ is strictly well-founded. That is, whenever $b$ is a non-empty subset of $A$, $b$ has a strictly minimal element under $\prec$.