Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 143 / 4 / c / Solution

For the standard generator $1$ of the additive group $\mathbb{Z}$, take the intervalsOnly the two endpoints change under translation by $1$, and henceThe same follows for every fixed integer translation by iteration. Therefore these sets are a Følner sequence for the integers, and $\mathbb{Z}$ satisfies the Følner condition.