# 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 $A$ if and only if:

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