Limits pp 50-59 | Cite as

Bisection Arguments

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


This chapter contains three important results: (1) the Intermediate Value Theorem (that if a continuous function takes the values a and b, then it takes all values between a and b); (2) a function whose derivative is identically zero is constant; (3) the General Principle of Convergence (which gives a necessary and sufficient condition for a limit to exist). All of these are proved by the repeated bisection of an interval.


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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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