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| Definition: Partial Order (see PoSet for partially ordered set). |
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}