Definition 1.4.16.  Let S be a set, ⪯ be a relation on S. We define:
⪯ is a total order  :⇔  ⪯ is connex and ⪯ is antisymmetric and ⪯ is transitive  ⇔  ⪯ is a partial order and ⪯ is connex
Equivalence.  No proof.
References.