Definition of lim inf $f_n$ I am having difficulty understanding what $\liminf f_n$ means where $f_n$ is a sequence of functions.  I understand what it means for a sequence of points, just not for a sequence of functions.
Thank you

In the context you're looking at: $$\displaystyle \liminf_{n \to \infty} f_n = \sup_{n \geq 0} \inf_{m \geq n} f_m$$ pointwise.
In our case, the variable that is changing is the function, if the variable that's changing is the value passed into the function we would have: $$\liminf_{y \to x} f(y) = \sup_{\delta > 0} \inf_{\vert y - x \vert < \delta} f(y).$$
