Completeness of normed spaces

As earlier, I have actually obtained a solution from this website that Bolzano Weierstrass' theory holds true for limited dimensional normed rooms, yet except boundless dimensional rooms. This, specifically = > all limited dim. normed rooms are full (in the feeling that every Cauchy series merges (w.r.t. standard) ). Nonetheless, is it real that every normed vector room is full?