User:Ascii/Coprime Relation for Integers is Non-Reflexive

Theorem
The relation "is coprime to" on the integers is non-reflexive.

That is, it is neither reflexive:


 * $\exists n \in \Z: \neg n \perp n$

nor antireflexive:


 * $\exists n \in \Z: n \perp n$

where $\perp$ denotes "is coprime to".