| 释义 |
Cauchy sequence A real (or complex) sequence {an} is Cauchy if |an−am| tends to 0 as m,n tend to infinity. A real (or complex) sequence is Cauchy if and only if it is convergent. The definition has the merit of implying convergence without explicit knowledge of the limit. Generally, in a metric space, Cauchy sequences can be defined using the distance d(an,am) instead. See complete metric space.
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