Definition:Well-Founded Ordered Set

Definition
Let $\left({S, \preceq}\right)$ be a poset.

Then $\left({S, \preceq}\right)$ is well-founded iff every non-empty subset of $S$ has a smallest element.

The term well-founded can equivalently be said to apply to the ordering $\preceq$ itself rather than to the poset as a whole.

Also see

 * Well-Ordering
 * Well-Ordered Set