Cauchy Sequence

A Sequence $a_1$, $a_2$, ... such that the Metric $d(a_m,a_n)$ satisfies

$$\lim_{\min(m,n)\to\infty} d(a_m,a_n) = 0.$$

Cauchy sequences in the rationals do not necessarily Converge, but they do Converge in the Reals.

Real Numbers can be defined using either Dedekind Cuts or Cauchy sequences.

See also Dedekind Cut