Definition:Well-Orderable Set/Class Theory

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

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