Maximal element

Examples

• In Pareto efficiency, a Pareto optimum 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.
• In abstract algebra, the concept of a maximal common divisor is needed to generalize greatest common divisors to number systems in which the common divisors of a set of elements may have more than one maximal element.
• In computational geometry, the maxima of a point set are maximal with respect to the partial order of coordinatewise domination.