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单词 LowestUpperBound
释义

lowest upper bound


Let S be a set with a partial ordering , and let T be a subset of S. A lowest upper bound, or supremumMathworldPlanetmath, of T is an upper boundMathworldPlanetmath x of T with the property that xy for every upper bound y of T. The lowest upper bound of T, when it exists, is denoted sup(T).

A lowest upper bound of T, when it exists, is unique.

Greatest lower bound is defined similarly: a greatest lower bound, or infimumMathworldPlanetmath, of T is a lower bound x of T with the property that xy for every lower bound y of T. The greatest lower bound of T, when it exists, is denoted inf(T).

If A={a1,a2,,an} is a finite setMathworldPlanetmath, then the supremum of A is simply max(A), and the infimum of A is equal to min(A).

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更新时间:2025/5/4 16:31:49