Definition: Partial Order (see PoSet for partially ordered set).
A relation $\le$ is a partial order on a set $S$ if it has: \begin{enumerate} \item Reflexivity: $a \le a$ for all $a \in S$. \item Antisymmetry: $a \le b$ and $ b \le a \Rightarrow a=b$. \item Transitivity: $a \le b$ and $b \le c \Rightarrow a \le c$. \end{enumerate}