How to prove whether this function is continuous or not? $$f(x)=
\begin{cases}
2, \mbox{  } (\forall) \mbox{ } x\in \mathbb{Q}\\
-2, \mbox{  } (\forall) \mbox{ } x\in \mathbb{R}\setminus \mathbb{Q}
\end{cases}
$$
Usually piece wise functions can be checked for continuity by taking limit at the end points of the intervals. But, how to do this problem? Please give me some hints. 

It is not continuous.
Hint:
For any $x \in \Bbb R \setminus \Bbb Q$, there exists $\{x_n: x_n \in \Bbb Q\}$ converges $x$, then $f(x_n)=2 \not= -2=f(x)$.
