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The Real Numbers

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More Calculus of a Single Variable

Part of the book series: Undergraduate Texts in Mathematics ((UTM))

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Abstract

We assume that the reader has some familiarity with the set of real numbers, which we denote by R. We review interval notation, absolute value, rational and irrational numbers, and we say a few things about sequences. The main point of this chapter is to acquaint the reader with two very important properties of R: the Increasing Bounded Sequence Property, and the Nested Interval Property.

Everything is vague to a degree you do not realize till you have tried to make it precise.

—Bertrand Russell

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Authors and Affiliations

  1. Mathematics Department, SUNY Buffalo State, Buffalo, NY, USA

    Peter R. Mercer

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  1. Peter R. Mercer
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Mercer, P.R. (2014). The Real Numbers. In: More Calculus of a Single Variable. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1926-0_1

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