Definition:Infimum of Mapping/Real-Valued Function

Definition
Let $f: S \to \R$ be a real-valued function.

Let $f$ be bounded below on $S$.

Also defined as
Some sources refer to the infimum as being the lower bound. Using this convention, any element greater than this is not considered to be a lower bound.

Linguistic Note
The plural of infimum is infima, although the (incorrect) form infimums can occasionally be found if you look hard enough.

Also see

 * Continuum Property, which guarantees that this infimum always exists.


 * Equivalence of Definitions of Infimum of Real-Valued Function


 * Definition:Supremum of Real-Valued Function


 * Definition:Infimum of Mapping
 * Definition:Supremum of Mapping