Definition:Well-Ordering

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

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

If this is the case, then $$\left({S, \preceq}\right)$$ is referred to as a well-ordered set or woset.

Also see

 * Well-Ordering is Total Ordering, which shows that every well-ordering is in fact a total ordering.