Sequences of Real Numbers

Mariano Giaquinta and Giuseppe Modica
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Mariano Giaquinta: Scuola Normale Superiore, Dipartimento di Matematica
Giuseppe Modica: Università degli Studi di Firenze, Dipartimento di Matematica Applicata

Chapter 2 in Mathematical Analysis, 2004, pp 31-70 from Springer

Abstract: Abstract As we have seen, we can represent any rational number, for instance $$\sqrt 2 $$ , by its successive approximations with rational numbers, q1, q2, .... According to Greek mathematicians the process which generates the approximations q1, q2, ... never ends; for us, instead, such a process is the realization of $$\sqrt 2 $$ as the limit of the sequence {q n }. In this chapter we shall discuss the notions of sequence and of limit of a sequence.

Keywords: Rational Number; Cauchy Sequence; Convergent Subsequence; Monotone Sequence; Recursive Definition (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-8176-4414-7_2

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