Partial Order

algebra

Definition

Partial Order

A relation $R$ is a partial order if the following properties are fulfilled:

• reflexive: $\forall a:aRa$
• antisymmetric: $\forall a,b:aRb\wedge bRa⟹a=b$
• transitive: $\forall a,b,c:aRb\wedge bRc⟹aRc$

Example:

$$aRb:⟺a\le b$$

A partial order is called total order if $\forall a,b:aRb\vee bRa$.