Theorem If a Best Approximation exists, then it is unique. Prove Uniqueness Suppose there exists two Best Approximations a,a′. To show a=a′, it suffices to show ⟨a−a′∣a−a′⟩=0 ⟨α−a′∣a−a′⟩=⟨β−β+a−a′,a−a′⟩=⟨β−a∣,a−a′⟩−⟨β−a∣a−a′⟩=0−0=0 Thus, a−a′=0⟹a=a′