Examples
- In Pareto efficiency, a Pareto optimal is a maximal element with respect to the partial order of Pareto improvement, and the set of maximal elements is called the Pareto frontier.
- In decision theory, an admissible decision rule is a maximal element with respect to the partial order of dominating decision rule.
- In modern portfolio theory, the set of maximal elements with respect to the product order on risk and return is called the efficient frontier.
- In set theory, a set is finite if and only if every non-empty family of subsets has a minimal element when ordered by the inclusion relation.
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