That's what I originally wrote in post 7. I showed $\displaystyle \phi_n$ was incomplete. But that's ok, because if $\displaystyle \phi_n$ is incomplete, $\displaystyle \widehat{\phi}_n$ is incomplete because you can't create a complete basis using only an incomplete basis.

There is another way to show $\displaystyle \phi_n$ is incomplete using theorem from my previous post. Show (f,$\displaystyle \phi_n$) = 0 for a non-zero f. take f(x) = 0 for x>0 and f(x) =1 for a<= x <=0, any a.

NOTE: finally figured out how to write $\displaystyle \phi_n$. I copied the code and tried it in a practice post and wrapped it in [tex] tags and it simply did not work. Then tried [TEX] tags and it worked. Now I can communicate a little more intelligibly.

BY the way, when I tried to reply on my other computer, Forum locked up on me again. I noticed a current thread about hacking. Maybe something is around.