is an orthogonal set in (prove it) and so remember that if and are orthogonal vectors (Because is a Hilbert sapce).
Is the sequence {sin(nx)} Cauchy in L2 over [0,pi]? Why or why not?
Under the L2 norm, this would amount to the integral of |sin(nx)-sin(mx)|^2 from 0 to pi being bounded by small epsilon for all n,m > N, right?
I can't figure this guy out. Thanks for any help in advance.