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| {{{#!latex2 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} }}} |
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 $$b \le c \Rightarrow a \le c$$. |
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 $$b \le c \Rightarrow a \le c$$.