- #1
homology
- 306
- 1
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?
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?