# Cauchy sequence

*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.*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 $k,\; m\; ge\; N$ : $d(x\_k,\; x\_m)\; <\; epsilon$.

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