Completeness A sequence which satisfies the Cauchy condition is called a Cauchy sequence . Therefore, every sequence which has a limit is a Cauchy sequence. This property of the real number system is called completeness . We may regard the infinite decimals which represent real numbers as special Cauchy sequences. This represents the real number sqrt 2, because sqrt 2 is the limit of the sequence.
Every bounded sequence has a subsequence with a limit.
We also say the series converges to s . A series which is not summable is said to diverge . But the converse is false. By R. H. B. Exell, 1998. King Mongkut's University of Technology Thonburi.