Sequences of Real Numbers

  • Mariano Giaquinta
  • Giuseppe Modica


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.


Rational Number Cauchy Sequence Convergent Subsequence Monotone Sequence Recursive Definition 
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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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