Discussion:
Q: Suppose f(x) and g(x) are continuous real-valued functions defined for [0,1]. Define vectors in n, F= ( f(x1), f(x2), ...,f(xn)) and G= g(x1), g(x2), ...,g(xn)), where xk = k/n. Why is n = 1/n Σ f(xk) g(xk) dx not an inner product for the space of continuous functions?