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On the Removal of Infinities from Divergent Series

Natiello, Mario LU and Solari, Hernán G. (2015) In Philosophy of Mathematics Education Journal 29. p.13-13
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.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
divergent series, Signification
categories
Higher Education
in
Philosophy of Mathematics Education Journal
volume
29
pages
13 - 13
publisher
University of Exeter. School of Education
ISSN
1465-2978
language
English
LU publication?
yes
id
497f9d58-c639-4d5c-a040-f5e619d2ead9 (old id 7855004)
alternative location
http://people.exeter.ac.uk/PErnest/
date added to LUP
2015-09-09 12:28:55
date last changed
2017-03-14 13:42:25
@article{497f9d58-c639-4d5c-a040-f5e619d2ead9,
  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.},
  author       = {Natiello, Mario and Solari, Hernán G.},
  issn         = {1465-2978},
  keyword      = {divergent series,Signification},
  language     = {eng},
  pages        = {13--13},
  publisher    = {University of Exeter. School of Education},
  series       = {Philosophy of Mathematics Education Journal},
  title        = {On the Removal of Infinities from Divergent Series},
  volume       = {29},
  year         = {2015},
}