# Math Help - Sequence of functions

1. ## Sequence of functions

Construct a sequence of functions on [0,1] each of which is discontinuous at every point of [0,1] and which converges uniformly to a function that is continuous at every point.

Can anyone help?

2. Originally Posted by problem
Construct a sequence of functions on [0,1] each of which is discontinuous at every point of [0,1] and which converges uniformly to a function that is continuous at every point.

Can anyone help?
$f_n(x)=\bigg\{\begin{array}{lr}1/n:&x\in\mathbb{Q}\\0:&x\notin\mathbb{Q}\end{array }$