Limits and Continuity

Mariano Giaquinta and Giuseppe Modica
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Mariano Giaquinta: Scuola Normale Superiore
Giuseppe Modica: Università degli Studi di Firenze, Facoltà di Ingegneria

Chapter 2 in Mathematical Analysis, 2003, pp 65-92 from Springer

Abstract: Abstract This chapter deals with the concepts of limit and continuity for real functions of one real variable. In Section 2.1 we introduce the notion of limit, we discuss some of the elementary properties, especially in connection with the order and the algebraic operations in ℝ, and finally, we prove that monotone functions always have limits. In Section 2.2 we illustrate the notion of continuous functions and show how interaction of continuity of functions with continuity of reals allows us to identify situations in which it is simple to guarantee the existence of (i) solutions of general equations as ƒ(x) = 0, (ii) points at which a function attains its maximum and its minimum.

Keywords: Continuous Function; Monotone Function; Qualitative Property; Invertible Function; Continuity Figure (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0007-9_2

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DOI: 10.1007/978-1-4612-0007-9_2

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