On the Removal of Infinities from Divergent Series
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7855004
- author
- Natiello, Mario LU and Solari, Hernán G.
- organization
- publishing date
- 2015
- 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
- 2016-04-01 14:02:46
- date last changed
- 2018-11-21 20:22:32
@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}}, keywords = {{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}}, url = {{http://people.exeter.ac.uk/PErnest/}}, volume = {{29}}, year = {{2015}}, }