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Let B, D be a metric space, e be any positive number, m be an integer such that m Є N where N is the set of all positive integers, and let {sb}, b Є Nand {sc}, c Є N be sequences where both b and c are greater than m. Then the sequence {sb} is a Cauchy sequence in the set B with metric D if for any element e Є B, an m exists where D(sb,sc) < e
That's just a fancy way of saying converging sequences are Cauchy sequences, but not necessarily the other way around.
See related links for some definitions.
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