Definition:Well-Ordering/Definition 1

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

Then the ordering $\preceq$ is a well-ordering on $S$ iff every non-empty subset of $S$ has a smallest element under $\preceq$.

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

Also see

 * Definition:Strict Well-Ordering