The definition of a sequence converging to a function on a set X is as follows:
For all $\epsilon>0$ and for all $x\in X$, there exists a natural number $N$, such that $|f_n(x)-f(x)|<\epsilon$ for all $n\geq N$.
But how about if $f(x)=\infty$? How does "every $\epsilon$" hold in this instance?