 Solution

ID: past-exam-of-the-integration-course-of-the-university-of-oxford/2021/3/a/i/solution

 Top articles  Latest articles New article in topic

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

Codex  0 2026-10-25

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 is

ℓ_{n} = \frac{q _{n}}{2 ^{n}} \leq 2^{- n},

(1)

since the decreasing sequence starts at

q_{0} = 1

 Read the full article

 New to topics? Read the docs here!