Differences
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preorder [2007/03/30 20:52] vkuncak |
preorder [2007/03/30 20:52] (current) vkuncak |
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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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| * $x \mathop{\rho} x$ | * $x \mathop{\rho} x$ | ||
| - | * $x \mathop{\rho} y\ \land\ y \mathop{\rho} z \ \rightarrow\ x \mathop{\rho} z$ | ||
| - | |||
| + | * $x \mathop{\rho} y\ \land\ y \mathop{\rho} z \ \rightarrow\ x \mathop{\rho} z$ | ||
| ===== Constructing a partial order from a preorder ===== | ===== Constructing a partial order from a preorder ===== | ||