question 4, please

4. Assume the notation and hypotheses of Page 88, # 6. Prove there exists a unique x E R such that a;, b;] = {x}. This result is called the Nested Interval Theorem. j=1 6. Assume that we have intervals [a1, bj] 2 [a2, b2] 2 ..., each of positive length, and that limj +cola; - b;| =0. Prove that there is a point a such that @ ( [aj, bj] for every j