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Subsequence

  • Definition: Let s={s_n} be an infinite sequence, and let k be a function whose domain is the set of positive integers and whose range is a subset of the positive integers. Assume that k is "order-preserving," that is, assume that k(m) < k(n), if m < n. Then the composite function s(k(n)) = s_(k(n)). Such a composite function is said to be a subsequence of s.

    Source: Mathematical Analysis, second edition by Tom M. Apostol

  • Listed under: Mathematical Analysis, Field Of Topology

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