Definition 1.4.18.  Let S be a set, ≺ be a relation on S, T ⊆ S, s ∈ S. We define:
s is a ≺-upper bound of T  :⇔  ∀ t ∈ T : t ≺ s  ⇔  s is a ≺T-lower bound of T
Equivalence.  No proof.