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Supremum (least upper bound)

The supremum of a subset X of a partially ordered set is the least element that is greater than or equal to every element of X, when such an element exists. It generalises the maximum and is used in order theory and real analysis.

s=\sup(X)

What the symbols mean

the supremum of X
a subset of the partially ordered set (K, \preceq)
the underlying set of the partially ordered set (K, \preceq)
the partial order relation on K
the set of all upper bounds of X
an arbitrary upper bound of X in U

About this formula

  • FieldMathematics
  • TopicOrder theory
  • LevelUniversity
  • Also calledsup, least upper bound, lub, supremum of a set, least upper bound definition
  • SourceWikidata Q215071

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