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{{{#!latex
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}
}}}		 A relation $$\le$$ is a partial order on a set $$S$$ if it has:
 * Reflexivity: $$a \le a$$ for all $$a \in S$$.
 * Antisymmetry: $$a \le b$$ and $$b \le a \Rightarrow a=b$$.
 * Transitivity: $$a \le b$$ and $$b \le c \Rightarrow a \le c$$.

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

A relation $$\le$$ is a partial order on a set $$S$$ if it has:

  • Reflexivity: $$a \le a$$ for all $$a \in S$$.
  • Antisymmetry: $$a \le b$$ and $$b \le a \Rightarrow a=b$$.
  • Transitivity: $$a \le b$$ and $$b \le c \Rightarrow a \le c$$.

PartialOrder (last edited 2020-01-26 22:54:17 by scot)