Order Relation

Last updated Nov 1, 2022

Let $P$ be a Set and let $R \subset P \times P$ be a Relation on $P$. Then $R$ is an Order Relation if $R$ is a Preorder Relation and the following holds:

• Antisymmetry: Let $x, y \in P$. If $xRy$ and $yRx$ then $x=y$

• Every Preorder Relation induces an Order Relation