Prove or disprove.
$\forall n \in \mathbb N$, $\forall \epsilon >0$, $\exists \delta >0$ such that $\forall x,y \in [0,1]$
$|x-y| < \delta$ implies that $|f_n(x)-f_n(y)| < \epsilon$.
I am pretty sure this is false because the limit function is not continuous and this problem is basically asking about the continuity of each approximating function in the sequence of functions.
How would I formally prove this??