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Introduction

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Elementary Analysis

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

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Abstract

The underlying space for all the analysis in this book is the set of real numbers. In this chapter we set down some basic properties of this set. These properties will serve as our axioms in the sense that it is possible to derive all the properties of the real numbers using only these axioms. However, we will avoid getting bogged down in this endeavor. Some readers may wish to refer to the appendix on set notation.

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Notes

  1. 1.

    Polynomials like this, where the highest power has coefficient 1, are called monic polynomials.

  2. 2.

    An integer p ≥ 2 is a prime provided the only positive factors of p are 1 and p.

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Authors and Affiliations

  1. Department of Mathematics, University of Oregon, Eugene, OR, USA

    Kenneth A. Ross

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Ross, K.A. (2013). Introduction. In: Elementary Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6271-2_1

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