Definition:Bounded Above Mapping/Real-Valued

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

$f$ is bounded above on $S$ by the upper bound $H$ :
 * $\forall x \in S: \map f x \le H$

That is, the set $\set {\map f x: x \in S}$ is bounded above in $\R$ by $H$.

Also see

 * Definition:Upper Bound of Real-Valued Function


 * Definition:Bounded Below Real-Valued Function
 * Definition:Lower Bound of Real-Valued Function


 * Definition:Bounded Real-Valued Function