\chi _\mathbb{Q} :\left[ {0,1} \right] \to \left\{ {0,1} \right\},\chi _\mathbb{Q} \left( x \right) = \left\{ \begin{gathered}
 1,x \in \mathbb{Q} \hfill \\
 0,x \in \mathbb{R}\backslash \mathbb{Q} \hfill \\ 
\end{gathered} \right.