Choose a closed interval containing the <bounded sequence>. Bisect it and retain a half containing infinitely many terms; repeat. The resulting intervals are nested and their lengths tend to zero. By the <nested interval theorem> they have one common point $x$, and choosing successively indexed terms from these intervals produces a subsequence converging to $x$. This proves the <Bolzano-Weierstrass theorem>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2020 / ia / Paper 1 / 10F / a / Solution

 Solution (source code)