1. The problem statement, all variables and given/known data Deduce that (P[0,1], norm(inf)) is not complete. 2. Relevant equations 3. The attempt at a solution I am not really sure how to start this. My strongest instinct is to find a polynomial that converges to something that isn't a polynomial (discontinuous, trigonometric, or whatever). I have no tools to find such a polynomial without the 'needle in a haystack' approach. Every Cauchy sequence is bounded, so trying to find an unbounded element of P[0,1] is out. Any direction to steer this ship in would be appreciated.