> [!NOTE] Definition (Total Order) > A [[Binary Relation|binary relation]] is a total order iff it is [[Reflexive Relation|reflexive]], [[Antisymmetric Relation|antisymmetric]], [[Transitive Relation|transitive]], and [[Total Relation|total]]. > > In other words a [[Partial Order|partial order]] relation that is additionally total. > [!Example] Examples > The relation of $\leq$ on $\mathbb{N}$ is a total order.