Infimum

In mathematics the infimum of a subset of some set is the greatest element, not necessarily in the subset, that is smaller than all other elements of the subset. Consequently the term greatest lower bound (also abbreviated as glb or GLB) is also commonly used. Infima of real numbers are a common special case that is especially important in analysis. However, the general definition remains valid in the more abstract setting of order theory where arbitrary partially ordered sets are considered.

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Infima are in a precise sense dual to the concept of a supremum and thus additional information and examples are found in that article.

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Subset: In mathematics, especially in set theory, a set A is a subset of a set B, if A is "contained" inside B. The relationship of one set being a subset of another is called inclusion....

Greatest element: In mathematics, especially in order theory, the greatest element of a subset S of a partially ordered set (poset) is an element of S which is greater than or equal to any other element of S. The term least element is defined dually. A bounded poset is a poset that has both a greatest element and a l...

Real number: In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. The term "real number" is a retronym coined in response to "imaginary number"....