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Limits pp 99-115 | Cite as

Sequences

  • Alan F. Beardon
Chapter
  • 1.2k Downloads
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

We discuss convergent sequences, give some examples, and then prove the fundamental result that every bounded sequence has a convergent subsequence. This is then used to prove that every nonconstant complex polynomial has a complex root. Finally, we discuss what is meant by a sequence converging to ∞.

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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Alan F. Beardon
    • 1
  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeEngland, UK

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