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Sequences of Real Numbers

  • Mariano Giaquinta
  • Giuseppe Modica

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Mariano Giaquinta
    • 1
  • Giuseppe Modica
    • 2
  1. 1.Dipartimento di MatematicaScuola Normale SuperiorePisaItaly
  2. 2.Dipartimento di Matematica ApplicataUniversità degli Studi di FirenzeFirenzeItaly

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