Definition:Well-Orderable Set

Definition
Let $S$ be a set.

If it is possible to construct an ordering $\preceq$ on $S$ such that $\preceq$ is a well-ordering, then $S$ is defined as being well-orderable.

Also see

 * The Well-Ordering Theorem, which states that every set $S$ is well-orderable.


 * The Axiom of Choice, which states that every set of sets can have a choice function associated with it.


 * The Well-Ordering Theorem is Equivalent to Axiom of Choice &mdash; assuming the truth of one, you can prove the other.