Definition:Upper Bound of Mapping

Definition
Let $f: S \to T$ be a mapping whose codomain is an ordered set $\left({T, \preceq}\right)$.

Let $f$ be bounded above in $T$ by $H \in T$.

Then $H$ is an upper bound of $f$.

Real-Valued Function
The concept is usually encountered where $\left({T, \preceq}\right)$ is the set of real numbers under the usual ordering: $\left({\R, \le}\right)$:

Also see

 * Definition:Bounded Above Mapping


 * Definition:Bounded Below Mapping
 * Definition:Lower Bound of Mapping


 * Definition:Bounded Mapping