Real Numbers and Natural 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 1 in Mathematical Analysis, 2004, pp 1-30 from Springer

Abstract: Abstract 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.

Keywords: Natural Number; Nonempty Subset; Irrational Number; Axiomatic Approach; Pythagorean Theorem (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4414-7_1

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DOI: 10.1007/978-0-8176-4414-7_1

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