Let (xk) ⊂ Rn and x ∈ Rn: Show that xk → x in Rn if and only if for every y ∈ Rn the

Question

sequence (⟨xk; y⟩) ⊂ R converges to ⟨x; y⟩, that is, ⟨xk; y⟩ → ⟨x; y⟩ in R.