# Cauchy sequence

1. Noun.  (analysis) A sequence in a normed vector space such that the difference between any two entries can be made arbitrarily small by stipulating that the two entries be sufficiently far out in the sequence.
2. Noun.  (analysis) A sequence $x_n$ in a metric space with metric ''d'' such that for every $epsilon > 0$ there exists a natural number ''N'' so that for every $k, m ge N$ : $d\left(x_k, x_m\right) < epsilon$.

This is an unmodified, but possibly outdated, definition from Wiktionary and used here under the Creative Commons license. Wiktionary is a great resource. If you like it too, please donate to Wikimedia.

This entry was last updated on RefTopia from its source on 3/20/2012.