Definition:Well-Ordering

Let $$\left({S; \preceq}\right)$$ be a toset.

Then the total 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.