infimumn.
/ɪnˈfʌɪməm/ Mathematics.
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.
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > elements in or parts of
interval1838
identity1894
identity element1902
complement1937
supremum1938
infimum1940
sup1940
equivalence class1952
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. Topol. 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. Topol. 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 <1, 3, 5,…;…, 6, 4, 2>, there is no infimum to the set of even numbers even though they are bounded below.
1964 W. J. Pervin Found. Gen. Topol. i. 15 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.
This entry has not yet been fully updated (first published 1976; most recently modified version published online June 2018).
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n.1940