Definition:Reflexive Partial Ordering

Definition
Let $S$ be a set.

An reflexive partial ordering on $S$ is a relation $\mathcal R$ on $S$ such that:


 * $\mathcal R$ is reflexive, that is, $\forall a \in S: a \mathcal R a$
 * $\mathcal R$ is transitive, that is, $\forall a, b, c \in S: a \mathcal R b \land b \mathcal R c \implies a \mathcal R c$

Also see
Compare this with an ordering, which, as well as being reflexive and transitive, is also antisymmetric.