# Definition:Strict Well-Ordering/Definition 2

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## Definition

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.