Real Numbers and Natural Numbers

  • Mariano Giaquinta
  • Giuseppe Modica


In this chapter, after an introductory section, in Section 1.2 we shall illustrate the axiomatic approach to real numbers, and, in Section 1.3, we shall identify the natural numbers as the smallest inductive subset of ℝ. Further information about natural numbers will be discussed in Chapter 3, while the notions of sequences and of limit of a sequence, which are specially relevant in mathematics, are discussed in Chapter 2; in Section 2.2 we present, in particular, several equivalent formulations of the continuity axiom.


Natural Number Nonempty Subset Irrational Number Axiomatic Approach Pythagorean Theorem 
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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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