- Thread starter
- #1

- Jan 17, 2013

- 1,667

\(\displaystyle

f(x) =

\begin{cases}

0 & \text{if } x \in \mathbb{Q} \\

1 & \text{if } x \in \mathbb{R}-\mathbb{Q}

\end{cases}\)

\(\displaystyle

g(x) =

\begin{cases}

1 & \text{if } x \in \mathbb{Q} \\

0 & \text{if } x \in \mathbb{R}-\mathbb{Q}

\end{cases}\)

\(\displaystyle f,g\) are continous nowhere but \(\displaystyle h(x)=0 \,\,\, \, \forall \,\, x \in \mathbb{R}\).

What other examples you might think of ?