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Is every absolutely convergent series convergent?

Published online by Cambridge University Press:  22 September 2016

G. L. Cohen
G. L. Cohen*
Affiliation:
School of Mathematical Sciences, The New South Wales Institute of Technology, Sydney, Australia
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Extract

There are various ways of introducing a discussion of the completeness of the system of real numbers. In this article we take the unusual approach suggested by the provocative question of the title.

In any elementary treatment of the convergence of sequences and series, a discussion of series of positive and negative terms will lead to the theorem that an absolutely convergent series is convergent.

Type
Research Article
Information
The Mathematical Gazette , Volume 61 , Issue 417 , October 1977 , pp. 204 - 213
Copyright
Copyright © Mathematical Association 1977

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References

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2. Kuller, Robert G., Topics in modern analysis. Prentice-Hall (1969).Google Scholar
3. Maddox, I. J., Elements of functional analysis. Cambridge University Press (1970).Google Scholar