Hi, I'm having trouble to write a formal proof for the following.

1. Let $\displaystyle f(x)=\left\{\begin{array}{cc}0,&\mbox{ if x is irrational}

\\1, & \mbox{ if x is rational} \end{array}\right.$. Show that $\displaystyle \lim \limits_{x \rightarrow a} f(x)$ does not exist for any a

*EDIT* I deleted the second problem so I could posted without double-posting