# Definition:Truncated Real-Valued Function

## Definition

Let $f: \R \to \R$ be a real function.

Let $m \in \Z_{>0}$ be a (positive) integer constant.

Let $f_m: \R \to \R$ be the real function defined as:

$\forall x \in \Dom f: \map {f_m} x = \begin {cases} \map f x & : \map f x \le m \\ m & : \map f x > m \end {cases}$

Then $\map {f_m} x$ is called (the function) $f$ truncated by $m$.