Abstract
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
Apostol, T., “Mathematical Analysis”, Addison-Wesley, Inc., Reading, Mass. (1960).
Buck. R., “Advanced Calculus”, (Second Ed.), McGraw-Hill, Inc. New York (1965).
Devinatz, A., “Advanced Calculus”, Holt, Reinhart and Winston, Inc., New York (1968).
Hight, D., “A Concept of Limits”, Prentice-Hall, Inc., Engelwood Cliffs, N.J. (1966).
Widder, D., “Advanced Calculus”, ( Second Ed. ), Prentice-Hall, Inc., Engelwood Cliffs, N.J. (1963).
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© 1979 Springer-Verlag New York Inc.
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Meyer, R.M. (1979). Behavior of a Function Near a Point: Various Types of Limits. In: Essential Mathematics for Applied Fields. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8072-6_5
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DOI: https://doi.org/10.1007/978-1-4613-8072-6_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90450-4
Online ISBN: 978-1-4613-8072-6
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