I have a question that I've come across and I'm having trouble with it. Any light anyone could shed on it would be an enormous help. The question is
(a)Show that a sequence (x(n)) where x(n) = (xn1, xn2) converges to x = (x1, x2) in R2 with the sup metric if and only if xn1 → x1 and xn2→ x2 in R.
(b)Prove that R2 with sup metric is complete
Any help would be appreciated