Cauchy sequence
A Cauchy sequence is a sequence whose terms ultimately become arbitrarily close together, after sufficiently many initial terms have been discarded. The notion of a Cauchy sequence is important in the study of sequences in metric spaces, and, in particular, in real analysis. One particularly important result in real analysis is the "Cauchy criterion for convergence of sequences": a sequence of real numbers is convergent if and only if it is a Cauchy sequence. This remains true in other complete metric spaces.