[…] a total order is a Binary relation \(\le\) on some set, \(X\), which satisfies the following \(\forall \; a,b,c \in X\):

  1. \(a \le a\): Reflexive
  2. \(a \le b\) and \(b \le c\) \(\implies\) \(a \le c\): Transitive
  3. \(a \le b\) and \(b \le a\) \(\iff\) \(a = b\): Antisymmetric relation
  4. \(a \le b\) or \(b \le a\): Strongly connected