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# Differences

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preorder [2007/03/30 20:52]
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preorder [2007/03/30 20:52] (current)
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A (reflexive) preorder relation $\rho$ on set $A$ is a binary relation $r \subseteq A^2$ that is reflexive and transitive, that is, these two properties hold: A (reflexive) preorder relation $\rho$ on set $A$ is a binary relation $r \subseteq A^2$ that is reflexive and transitive, that is, these two properties hold:
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* $x \mathop{\rho} x$   * $x \mathop{\rho} x$
-  * $x \mathop{\rho} y\ \land\ y \mathop{\rho} z \ \rightarrow\ x \mathop{\rho} z$
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+  * $x \mathop{\rho} y\ \land\ y \mathop{\rho} z \ \rightarrow\ x \mathop{\rho} z$

===== Constructing a partial order from a preorder ===== ===== Constructing a partial order from a preorder =====