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Uniformly Cauchy sequence

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 0 By others on same topic  0 Discussions  1970-01-01  See my version
A sequence \((x_n)\) in a metric space (or more generally, in a uniform space) is called a **uniformly Cauchy sequence** if for every positive real number \(\epsilon > 0\), there exists a positive integer \(N\) such that for all indices \(m, n \geq N\), the distance between the terms \(x_m\) and \(x_n\) is less than \(\epsilon\).

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