Null Function/Examples

Examples of Null Functions

Example 1

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.

Example 2

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

$\forall x \in \R: \map f x = \begin {cases} 1 & : t = 1 \\ 0 & : \text {otherwise} \end {cases}$

Then $f$ is a null function.

Example 3

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

$\forall x \in \R: \map f x = \begin {cases} 1 & : t = 1 \le t \le 2 \\ 0 & : \text {otherwise} \end {cases}$

Then $f$ is not a null function.