Null Function/Examples/Example 1

Example of Null Function
Let $f: \R \to \R$ be the real function defined as:
 * $\forall x \in \R: \map f x = \begin {cases} 1 & : t = 1/2 \\ -1 & : t = 1 \\ 0 & : \text {otherwise} \end {cases}$

Then $f$ is a null function.

Proof
Let $x > 1$.

The cases where $x < \dfrac 1 2$ and $\dfrac 1 2 \le x \le 1$ are treated similarly.