Viewing a finitely generated group as a metric space allows us to consider its growth function \(\gamma(n)\) which is the cardinality of the “ball” of radius \(\le n\) centred on the identity (the number of members of the group whose distance from the identity is not greater than \(n\)). A growth function for a given group depends on the set of generators chosen, but when the group is infinite the asymptotic behaviour as \(n \rightarrow \infty\) of the growth functions is independent of the set of generators.