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On the Removal of Infinities from Divergent Series

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Author

Summary, in English

The consequences of adopting other definitions of the concepts of sum and convergence of a series are discussed in the light of historical and epistemological contexts. We show that some divergent series appearing in the context of renormalization methods cannot be assigned finite values while preserving a minimum of consistency with standard summation, without at the same time obtaining contradictions, thus destroying the mathematical building (the conditions are known as Hardy’s axioms). We finally discuss the epistemological costs of accepting these practices in the name of instrumentalism.

Department/s

Publishing year

2015

Language

English

Pages

13-13

Publication/Series

Philosophy of Mathematics Education Journal

Volume

29

Document type

Journal article

Publisher

University of Exeter. School of Education

Topic

  • Other Mathematics

Keywords

  • divergent series
  • Signification

Status

Published

Research group

  • Analysis and Dynamics
  • Dynamical systems

ISBN/ISSN/Other

  • ISSN: 1465-2978