Limits

Steen Pedersen ()
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Steen Pedersen: Wright State University, Department of Mathematics

Chapter 1 in From Calculus to Analysis, 2015, pp 3-43 from Springer

Abstract: Abstract The set real numbers is defined as the set of infinite decimals. Density of the set of rational numbers and of the set of irrational numbers in the set of real numbers is established. This naturally leads to a discussion of accumulation points that serves as a precursor for the main part of this chapter: the theory of limits of functions. Convergence of sequences and series of numbers are discussed briefly. A bounded function, the Dirichlet function, that does not have a limit at any real number is presented. Section 1.8 contains a proof of Steinhaus’ three distance conjecture.

Keywords: Accumulation Point; Fractional Part; Arithmetic Progression; Irrational Number; Geometric Progression (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-13641-7_1

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