On the Removal of Infinities from Divergent Series

Mario Natiello, Hernán G. Solari

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)13
JournalPhilosophy of Mathematics Education Journal
Volume29
Publication statusPublished - 2015

Subject classification (UKÄ)

  • Other Mathematics

Free keywords

  • divergent series
  • Signification

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