Definition 1.4.21.  Let S be a set, ⪯ be a relation on S. We define:
⪯ is a well-order  :⇔  ⪯ is a total order and ∀ T ⊆ S s.t. T is nonempty : ∃ t ∈ T : t is a ⪯-least element of T
References.