Antireflexive Relation/Examples/Non-Equality

Example of Antireflexive Relation

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

Proof

We have:

$\forall a \in \N: \lnot \paren {a \ne a}$

Hence the result by definition of antireflexive relation.

Sources

• 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $1$: Sets and mappings: $\S 1.4$: Equivalence relations: Exercise $1 \ \text{(i)}$