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Infima

Greatest lower bound and least upper boundA set P{\displaystyle P} of real numbers (hollow and filled circles), a subset S{\displaystyle S} of P{\displaystyle P} (filled circles), and the infimum of S.{\displaystyle S.} Note that for totally ordered finite sets, the infimum and the minimum are equal.A set A{\displaystyle A} of real numbers (blue circles), a set of upper bounds of A{\displaystyle A} (red diamond and circles), and the smallest such upper bound, that is, the supremum of A{\displaystyle A} (red diamond).In mathematics, the infimum (abbreviated inf; pl.: infima) of a subsetS{\displaystyle S} of a partially ordered setP{\displaystyle P} is the greatest element in P{\displaystyle P} that is less than or equal to each element of S,{\displaystyle S,} if such an element exists.

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