let . then ||f|| = 0, but f ≠ 0.
What I have in my notes is that a norm on a vector space V is a function || ||:V to R satisfying x and y in V and for all scalars alpha. One of the axioms states that ||x||=0 IFF x vector = zero vector.
Hence the above function does not define a norm...not sure how to rigorously prove it though...?
THanks