Define a sequence of functions $f_n: (0,1)\rightarrow\mathbb{R}$ by
$\ f(x) = \begin{cases} 1/q^n & \text{if } x =p/q \space(\space\mathrm{nonzero})\\ 0 & \text{otherwise} \end{cases} $
Find the pointwise limit $f$ of $\{f_n\}$ and show $\{f_n\}$ converges uniformly.
$f$ looks like a modification of Thomae's function to me, but I can't see how a function that converges uniformly can also have a pointwise limit -- I thought uniform convergence was a stronger type of convergence?