A partial order on a set $E$ is a relation $⪯$ $E$ such that

1. for all $e\in E$, $e⪯e$
2. for all $e,f\in E$, if $e⪯f$ and $f⪰e$ then $e=f$
3. for all $e,f,g\in E$, if $e⪯f$ and $f⪯g$, then $e⪯g$