Past exam of the mathematics course of the University of Cambridge / 2016 / ib / Paper 4 / 3G / a / Solution

A contraction mapping on a metric space $(X,d)$ is a map $f:X\to X$ for which there is a single constant $q$ with $0\le q<1$ such thatThe same $q$ must work for every pair. Merely decreasing each nonzero distance strictly does not suffice for this definition.