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infimum

Noun

Meaning

English Wikipedia has an article on:infimumWikipedia
infimum (plural infima or infimums)

(mathematics) (of a subset) the greatest element of the containing set that is smaller than or equal to all elements of the subset. The infimum may or may not be a member of the subset.

Source: en.wiktionary.org

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Examples

Advanced : : : : If a set has a smallest element, as in the first example, then the smallest element is the infimum for the set. Source: Internet

By analogy with the above, in the domain of the extended reals, negative infinity is the identity element for the maximum and supremum operators, while positive infinity is the identity element for minimum and infimum. Source: Internet

Existence of an infimum of a subset of can fail if has no lower bound at all, or if the set of lower bounds does not contain a maximal element. Source: Internet

For instance, a lattice is a partially ordered set in which all finite subsets have both a supremum and an infimum, and a complete lattice is a partially ordered set in which all subsets have both a supremum and an infimum. Source: Internet

As the last three examples show, the infimum of a set does not have to belong to the set. Source: Internet

Definition for a set The limit inferior of a set X ⊆ Y is the infimum of all of the limit points of the set. Source: Internet

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