Alice in Numberland pp 141-160 | Cite as

# Sequences and Series— in which we discover very odd behaviour in even the smallest infinite set

Chapter

## Abstract

Much of the effort we have expended in developing the system ℝ of real numbers and in describing the infinite can now be put to good use. In this chapter we shall be investigating limiting processes, the very foundation of analysis. We begin by agreeing that an *infinite sequence* is a countably infinite set of real numbers occurring in some definite order, *a*_{1},*a*_{2},*a*_{3}, …, *a*_{ n }, …. Each *a*_{ i } *∈*ℝ and there is one *a*_{ i } for each *i*∈ℕ. A favoured abbreviation for a sequence is (*a* _{ n }), where *a*_{ n } denotes the *n*th term of the sequence.

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## Suggestions for Further Reading

- K. G. Binmore,
*Mathematical Analysis: A Straightforward Approach*, 2nd edition, Cambridge University Press (1982). One of the best beginner’s standard texts for proper analysis.CrossRefGoogle Scholar - A. Gardiner,
*Infinite Processes: Background to Analysis*, Springer (1982). A leisurely but thorough analysis of analysis! If you think you understand limits, this book will show you that you don’t—then provide you with a much more solid understanding.CrossRefGoogle Scholar - J. A. Green,
*Sequences and Series*, Routledge and Kegan Paul (1966). Packed full of examples of sequences and series.Google Scholar - H. E. Huntley,
*The Divine Proportion*, Dover (1970). If your appetite for the golden ratio has been whetted by this chapter, Huntley’s book goes a long way towards satisfying it.Google Scholar

## Copyright information

© John Baylis and Rod Haggarty 1988