Definition:Well-Ordering/Definition 2

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

Then the ordering $\preceq$ is a well-ordering on $S$ $\preceq$ is a well-founded total ordering.

Also see

 * Equivalence of Definitions of Well-Ordering


 * Definition:Well-Ordered Set
 * Definition:Strict Well-Ordering