【How-to】Is a constant sequence convergent

A Cauchy sequence need not converge. For example, consider the sequence (1/n) in the metric space ((0,1),|·|). Clearly, the sequence is Cauchy in (0,1) but does not converge to any point of the interval. … A metric space (X, d) is called complete if every Cauchy sequence (xn) in X converges to some point of X.