order

• pre-order
  • a tuple \((P, \leq_{P})\), where \(P\) is a set and \(\leq_{P}\) is a relation on \(P\) that is reflexive and transitve
• parital order (poset)
  • pre-ordered that is antisymmetric
• total order
  • a poset where the relation \(\leq_{P}\) is total