I'm ask to prove whether or not the sequence of functions defined on [-1,1] is pointwise convergent, where for each natural number n. I was hoping someone could look over my proof and see if I made any mistakes. The cases where x=0 and |x|=1 are obvious, so consider those as already proven.

Proof: Let be given and let where . Then, . Let N be a positive integer such that . Then, (I'm not 100% sure this is right, so please correct me if I'm wrong). So, for any positive integer , we have . Therefore, converges pointwise to the zero function on (-1,1)-{0}.