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Cauchy sequence []

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Wiktionary (2)

n (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.
n (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 .