A real (or complex) sequence {a_n} is Cauchy if |a_n−a_m| tends to 0 as m,n tend to infinity. A real (or complex) sequence is Cauchy if and only if it is convergent. The definition has the merit of implying convergence without explicit knowledge of the limit. Generally, in a metric space, Cauchy sequences can be defined using the distance d(a_n,a_m) instead. See complete metric space.