Antireflexive Relation/Examples

Examples of Antireflexive Relations

Non-Equality

The relation $\ne$ on the set of natural numbers $\N$ is antireflexive.

Strict Ordering

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

Distinctness

Let $S$ be a set.

Let $\RR$ be the relation on $S$ defined as:

$\forall x, y \in S: x \mathrel \RR y$ if and only if $x$ is distinct from $y$

Then $\RR$ is antireflexive.