Past exam of the integration course of the University of Oxford / 2021 / 3 / a / i / Solution

At stage zero there is one closed interval. At every later stage each component is replaced by two closed end intervals separated by a positive open gap. Induction therefore gives exactly $2^n$ pairwise disjoint closed intervals at stage $n$. Their common length issince the decreasing sequence starts at $q_0=1$.