Question 4.[2, 1, 2, 1 marks] Prove that (₁, 1) (l2, ||- ||2) as follows: (i) Let B., (0; 1) denote the open unit ball {x € l₁ | ||×||1₁ < 1}. Prove that it suffices to show that B|||₁ (0; 1) ~ (l2, ||· ||2₂). (ii) Suppose x := (₁, 2, n,) belongs to B₁.₁(0; 1). Prove that each com- ponent x₁ <1 for all i € N. (iii) Prove that x2 is finite by showing that ||x||2 < |x||1₁. (iv) Give a geometric interpretation.

Fig: 1