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Definition: Let (X, d) be a metric space. A sequence (x_n) of points of X is said to be a Cauchy sequence in (X, d) if it has the property that given epsilon greater than 0, there is an integer N such that d(x_n, x_m) is less than epsilon whenever n and m are greater than or equal to N.
Source: Topology (second edition) by James R. Munkres