In order to determine how far off from the real function we are, we need to estimate the norm of the function representing the difference between the real function and the approximation which tells us the magnitude of the difference. The value returned by the norm will be called the error. Practice and theory. Global error versus local error. Problems with using metrics instead of norms.
Norms relate to actual error.
Metrics may only be able to give an ordering. This is due to norms being linear with respect to scalar multiplication, and metrics not requiring this. It's not the same as assignment 1, but it does have some of the same issues. It can be found online here .