I'm finding that I'm not very good at showing that a space is complete. I was wondering if you could help me out. Consider the space of null sequences. That is, sequences of complex numbers that converge to zero. It has a max norm. So if x is a sequence the norm of x, |x| = max |a_n| where the max ranges over n. So we need to take a cauchy seqence of elements and show that it converges to a null sequence. I'm just not sure how to do it. Any hints?