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5 cards from this section. Quick, good the night before a test.
Define a cover in a poset.
Think about how elements relate directly in a Hasse diagram.
What is a maximal element?
What would happen to an element if nothing is above it?
What is an element cover in a poset?
Visualize it in a Hasse diagram.
True or False: A poset can have no minimal elements.
Think about the characteristics of infinite sets.
Create a poset with at least 6 elements, clearly identify the covers, maximal, minimal, greatest, and least elements.
Use a Hasse diagram approach for visualization.
Questioning a poset with no maximal element: construct and explain how it satisfies the properties of a poset.
Think about the direction and extent of the ordering relation.
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