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| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
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preorder [2007/03/30 20:35] vkuncak |
preorder [2007/03/30 20:40] vkuncak |
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| - | ===== Constructing partial order from a preorder ===== | + | ===== Constructing a partial order from a preorder ===== |
| Let $\rho$ be a preorder. Define relation $\sim$ by | Let $\rho$ be a preorder. Define relation $\sim$ by | ||
| Line 17: | Line 17: | ||
| P \leq Q\ \iff\ (\forall x \in P. \forall y \in Q. x \mathop{\rho} y) | P \leq Q\ \iff\ (\forall x \in P. \forall y \in Q. x \mathop{\rho} y) | ||
| \end{equation*} | \end{equation*} | ||
| - | for $P, Q \in A/_{\sim}$, then $\leq$ is a [[partial order]]. | + | for $P, Q \in A/_{\sim}$, then we can prove that $\leq$ is a [[partial order]]. |