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Sequences

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Abstract

A sequence is simply a set whose elements are labelled by the positive integers (though a more formal definition is given in the next section). We write a sequence in the form s = (s1,s2, s3,…) where the dots indicate that the list of terms continues indefinitely, so that any term, for instance s491, is available for consideration if required. More explicitly we write s = (s1, s2, s3,…, sn,…) to indicate the nth term, or simply s = (2n) 1 . But sn alone (no parentheses!) is not the name of a sequence, it is the name of a number which is the nth term of a sequence. For instance s = (2n - 1) 1 is the sequence of odd integers, s = (1,3,5,…) whose nth term is sn = 2n - 1.

Keywords

  • Cauchy Sequence
  • Convergent Subsequence
  • Peak Point
  • Convergent Sequence
  • Finite Limit

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2004 Springer-Verlag London

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Walker, P.L. (2004). Sequences. In: Examples and Theorems in Analysis. Springer, London. https://doi.org/10.1007/978-0-85729-380-0_1

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  • DOI: https://doi.org/10.1007/978-0-85729-380-0_1

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-493-2

  • Online ISBN: 978-0-85729-380-0

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