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Sets of Real Numbers

In: From Calculus to Analysis

Author

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  • Steen Pedersen

    (Wright State University, Department of Mathematics)

Abstract

Most of us believe we have a reasonable understanding of what a real number is. However, sets of real numbers have some deep and surprising properties. We will explore some of these properties in this chapter and in Chap. 4 on cardinality. Of notable interest for future applications are the order completeness of $\mathbb {R},$ the characterization of intervals in terms of the intermediate value property, and the nested interval theorem. Among other results we establish the existence of roots of positive real numbers and we introduce the amazing Cantor set as well as related functions.

Suggested Citation

  • Steen Pedersen, 2015. "Sets of Real Numbers," Springer Books, in: From Calculus to Analysis, edition 127, chapter 3, pages 51-68, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13641-7_3
    DOI: 10.1007/978-3-319-13641-7_3
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