Definition of infimum in English:



  • The largest quantity that is less than or equal to each of a given set or subset of quantities.

    The opposite of supremum
    • ‘Paman's explanation looks like our present definition of infimum and supremum, but whereas our infimum and supremum given a set (of real numbers) gives a real number, the Maximinus and Minimajus of a quantity is a quantity of the same kind.’
    • ‘Just as we proved that the supremum is unique, one can also show that the infimum is unique.’
    • ‘To ensure nondecreasing lower bounds, the hyper-rectangle to be bisected is chosen by selecting the region which contains the infimum of the minima of lower bounds.’
    • ‘The infimum may or may not be a member of the subset.’


1940s: from Latin, literally ‘lowest part’, neuter (used as a noun) of infimus ‘lowest’.