Given a metric space \((X,d)\). A sequence \((x_n)\) is called Cauchy sequence if for every \(\varepsilon>0\) a number \(n_0\in \mathbb{N}\) exists such that \(d(x_m,x_n)<\varepsilon\) for all \(m,n\ge n_0\).
A Cauchy sequence is a sequence where the distance between the values decreases for large \(n\in \mathbb{N}\).