Non-Reflexive Relation/Examples/Strict Ordering

Example of Antireflexive Relation
The relation $<$ on one of the standard number systems $\N$, $\Z$, $\Q$ and $\R$ is antireflexive.

Proof
We have:
 * $\forall a \in \N: \lnot \paren {a < a}$

Hence the result by definition of antireflexive relation.