Find a function $f:\Bbb R \to \Bbb R$ which is discontinuous at $1,\frac 12,\frac 13, ... $ but is continuous at every other point 
(a) Find a function $f:\Bbb R \to \Bbb R$ which is discontinuous at $1,\frac 12,\frac 13, ... $ but is continuous at every other point.
(b) Find a function $f:\Bbb R \to \Bbb R$ which is discontinuous at $1,\frac 12,\frac 13, ... $and $0$ but is continuous at every other point.


Hint: Try the functions $$f(x)=\begin{cases}x^2&:x=1/n,n\in\Bbb N\\ 0&:o.w.\end{cases}\quad\text{and}\quad g(x)=\begin{cases}1&:x=1/n,n\in\Bbb N\\ 0&:o.w.\end{cases}$$for $(a)$ and $(b)$ respectively.
