In mathematics, the infimum (plural infima) of a subset S of a partially ordered set T is the greatest element of T that is less than or equal to all elements of S. Consequently the term greatest lower bound (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.
If the infimum exists, it is unique. If S contains a least element, then that element is the infimum; otherwise, the infimum does not belong to S (or does not exist). For instance, the positive real numbers do not have a least element, and their infimum is 0, which is not a positive real number.
The infimum is in a precise sense dual to the concept of a supremum.
Read more about Infimum: Infima of Real Numbers, Infima in Partially Ordered Sets, Least Upper Bound Property