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.
| 1940 G. 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. 1949 S. 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. 1964 W. 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. 1968 E. T. Copson Metric Spaces i. 14 The infimum of a subset A is its greatest lower bound, and is denoted by inf A. |