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.

Related Topics:
Mathematics - Subset - Greatest element - Real number - Analysis - Order theory - Partially ordered set

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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.

Related Topics:
Dual - Supremum

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