Abstract
The chapter begins with a discussion of sequences that culminates in the concept of convergence, the fundamental concept of analysis. The Weierstrass-Bolzano theorem (§3.5), nominally a theorem about bounded sequences, is in essence a property of closed intervals; Cauchy’ criterion (§3.6) is a test for convergence, especially useful in the theory of infinite series (§10.1). The chapter concludes with a dissection of convergence into two more general limiting operations.
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© 1994 Springer Science+Business Media New York
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Berberian, S.K. (1994). Sequences of Real Numbers, Convergence. In: A First Course in Real Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8548-4_3
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DOI: https://doi.org/10.1007/978-1-4419-8548-4_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6433-0
Online ISBN: 978-1-4419-8548-4
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