would really appreciate help in understanding pointwise convergence and uniform convergence.
For example for the questions below, how does f_n converge pointwise to f(x)=0? To see whether a function converges pointwise or not, don't you just take the limits of the sequence of functions f_n. Because wouldn't lim(f_n(x))=infinity rather than than 0?
Could someone please also explain how one would check for uniform convergence. In this example, the function would be uniformly continuous since the function is defined over a compact set (closed and bounded interval) and is pointwise convergent. But is there another way to check for uniform convergence.
Your help would be greatly appreciated!