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词汇 infimum
释义

Definition of infimum in English:

infimum

noun ɪnˈfʌɪməm
Mathematics

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

    〔数〕下确界。SUPREMUM 的反义词

    The opposite of supremum
    Example sentencesExamples
    • Just as we proved that the supremum is unique, one can also show that the infimum is unique.
    • 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.
    • The infimum may or may not be a member of the subset.
    • 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.

Origin

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