英语词汇“infimum”的英英意思、用法、释义、翻译、读音、例句、短语、词组、英语词典-本地帮

单词

infimum

释义

infimum Math.|ɪnˈfaɪməm|
[L., = lowest part, neut. of infimus lowest (see infima species).]
The largest number that is less than or equal to each of a given set of real numbers; an analogous quantity for a subset of any other ordered set.
1940G. Birkhoff Lattice Theory ii. 16 We shall use the words ‘supremum’ and ‘sup’ synonymously with l.u.b.; similarly, we shall use ‘infimum’, and ‘inf’, and ‘common part’ synonymously with gr.l.b.1949S. Lefschetz Introd. Topology i. 27 We shall also use on occasion the supremum and infimum of a nonvoid set A of real numbers, written sup A, inf A.1964W. J. Pervin Found. Gen. Topology i. 15 In the natural ordering for the set of natural numbers, 2 is the infimum of the set of even numbers. In the case of the ordering , there is no infimum to the set of even numbers even though they are bounded below.Ibid., The rational numbers ordered by size are not order-complete, since the subset consisting of all rationals which are positive and have squares greater than 2 does not have an infimum, even though it is bounded below by 0.1968E. T. Copson Metric Spaces i. 14 The infimum of a subset A is its greatest lower bound, and is denoted by inf A.

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