Basic Real Analysis pp 39-96 | Cite as

# Sequences and Series of Real Numbers

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## Abstract

The elementary theories of real-valued functions of a real variable and of numerical sequences and series are treated in any standard calculus text. In most cases, however, the proofs are given in appendices and omitted from the main body of the course. To give rigorous proofs of the basic theorems on convergence, continuity, and differentiability, one needs a precise definition of real numbers. One way to achieve this is to start with the *construction* of real numbers from the rational ones by means of *Dedekind Cuts*.

## Keywords

Real Numbers Standard Calculus Text Rational Ones Dedekind Cuts Nested Interval Theorem
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## Copyright information

© Springer Science+Business Media New York 2014