The <Bolzano-Weierstrass theorem> states that \b[every bounded <sequence> in $\mathbb R$ has a convergent <subsequence>]. More generally, a bounded <sequence> in $\mathbb R^d$ has a <subsequence> converging to a point of $\mathbb R^d$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2011 / ia / Paper 1 / 3F / a / Solution

 Solution (source code)