# Differences

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 preorder [2007/03/30 20:52]vkuncak preorder [2007/03/30 20:52] (current)vkuncak Both sides previous revision Previous revision 2007/03/30 20:52 vkuncak 2007/03/30 20:52 vkuncak 2007/03/30 20:40 vkuncak 2007/03/30 20:40 vkuncak 2007/03/30 20:39 vkuncak 2007/03/30 20:35 vkuncak 2007/03/30 20:28 vkuncak 2007/03/30 20:28 vkuncak 2007/03/30 20:27 vkuncak created 2007/03/30 20:52 vkuncak 2007/03/30 20:52 vkuncak 2007/03/30 20:40 vkuncak 2007/03/30 20:40 vkuncak 2007/03/30 20:39 vkuncak 2007/03/30 20:35 vkuncak 2007/03/30 20:28 vkuncak 2007/03/30 20:28 vkuncak 2007/03/30 20:27 vkuncak created Line 2: Line 2: 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: + * $x \mathop{\rho} x$ * $x \mathop{\rho} x$ - * $x \mathop{\rho} y\ \land\ y \mathop{\rho} z \ \rightarrow\ x \mathop{\rho} z$ - + * $x \mathop{\rho} y\ \land\ y \mathop{\rho} z \ \rightarrow\ x \mathop{\rho} z$ ===== Constructing a partial order from a preorder ===== ===== Constructing a partial order from a preorder =====