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partial_order [2008/04/30 09:15] vkuncak |
partial_order [2008/04/30 10:00] vkuncak |
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| **Example:** Let $U = \{ 1,2,3\}$ and let $A = \{ \emptyset, \{1\}, \{2\}, \{3\}, \{2,3\} \}$. Then $(A, \le)$ is a partial order. We can draw it as a Hasse diagram. | **Example:** Let $U = \{ 1,2,3\}$ and let $A = \{ \emptyset, \{1\}, \{2\}, \{3\}, \{2,3\} \}$. Then $(A, \le)$ is a partial order. We can draw it as a Hasse diagram. | ||
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| + | ===== Hasse diagram ===== | ||
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| + | [[wk>Hasse diagram]] presents the relation as a directed graph in a plane, such that | ||
| + | * the direction of edge is given by which nodes is drawn above | ||
| + | * transitive and reflexive edges are not represented (they can be derived) | ||
| ===== Extreme Elements in Partial Orders ===== | ===== Extreme Elements in Partial Orders ===== | ||