Behavior of a Function Near a Point: Various Types of Limits

  • Richard M. Meyer
Part of the Universitext book series (UTX)


As is sometimes the case in Mathematics, the same (or similar) notation may be used for several different (though possibly related) concepts. Such is the case with the ‘lim inf’, ‘lim sup’ and ‘lim’ notation. We have already dealt with this notation (Sections 1–4) when considering sequences of sets, real numbers and real-valued functions. However, the same notation is also used in describing a different concept, related to the behavior of an individual real-valued function f near a single point x = c. In this Section, we examine this alternate concept of ‘lim inf’, ‘lim sup’ and ‘lim’, in an attempt to avoid possible confusion. Some (if not all) of the notions considered may be familiar.


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References to Additional and Related Material: Section 5

  1. 1.
    Apostol, T., “Mathematical Analysis”, Addison-Wesley, Inc., Reading, Mass. (1960).Google Scholar
  2. 2.
    Buck. R., “Advanced Calculus”, (Second Ed.), McGraw-Hill, Inc. New York (1965).Google Scholar
  3. 3.
    Devinatz, A., “Advanced Calculus”, Holt, Reinhart and Winston, Inc., New York (1968).Google Scholar
  4. 4.
    Hight, D., “A Concept of Limits”, Prentice-Hall, Inc., Engelwood Cliffs, N.J. (1966).Google Scholar
  5. 5.
    Widder, D., “Advanced Calculus”, ( Second Ed. ), Prentice-Hall, Inc., Engelwood Cliffs, N.J. (1963).Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Richard M. Meyer
    • 1
  1. 1.Niagara University, College of Arts and SciencesNiagara UniversityUSA

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