Uncommon
Infimum and supremum
Greatest lower bound and least upper bound
Infimum and supremum
In mathematics, the infimum (abbreviated inf; pl.: infima) of a subset S {\displaystyle S} of a partially ordered set P {\displaystyle P} is the greatest element in P {\displaystyle P} that is less than or equal to each element of S , {\displaystyle S,} if such an element exists. If the infimum of S {\displaystyle S} exists, it is unique, and if b is a lower bound of S {\displaystyle S} , then b is less than or equal to the infimum of S {\displaystyle S} . Consequently, the term greatest lower bound (abbreviated as GLB) is also commonly used. The supremum (abbreviated sup; pl.: suprema) of a subset S {\displaystyle S} of a partially ordered...
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