On the removal of infinities from divergent series

Autores
Natiello, Mario A.; Solari, Hernan Gustavo
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Natiello, Mario A.. Lund University; Suecia
Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Materia
SERIES
DIVERGENT
RENORMALIZATION
PHYSICS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/46148
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On the removal of infinities from divergent seriesNatiello, Mario A.Solari, Hernan GustavoSERIESDIVERGENTRENORMALIZATIONPHYSICShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The 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.Fil: Natiello, Mario A.. Lund University; SueciaFil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaUniversity of Exeter. School of Education2015-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/46148Natiello, Mario A.; Solari, Hernan Gustavo; On the removal of infinities from divergent series; University of Exeter. School of Education; Philosophy of Mathematics Education Journal; 29; 7-2015; 1-111465-2978CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/pome29/index.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:18:31Zoai:ri.conicet.gov.ar:11336/46148instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:18:31.372CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the removal of infinities from divergent series
title On the removal of infinities from divergent series
spellingShingle On the removal of infinities from divergent series
Natiello, Mario A.
SERIES
DIVERGENT
RENORMALIZATION
PHYSICS
title_short On the removal of infinities from divergent series
title_full On the removal of infinities from divergent series
title_fullStr On the removal of infinities from divergent series
title_full_unstemmed On the removal of infinities from divergent series
title_sort On the removal of infinities from divergent series
dc.creator.none.fl_str_mv Natiello, Mario A.
Solari, Hernan Gustavo
author Natiello, Mario A.
author_facet Natiello, Mario A.
Solari, Hernan Gustavo
author_role author
author2 Solari, Hernan Gustavo
author2_role author
dc.subject.none.fl_str_mv SERIES
DIVERGENT
RENORMALIZATION
PHYSICS
topic SERIES
DIVERGENT
RENORMALIZATION
PHYSICS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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.
Fil: Natiello, Mario A.. Lund University; Suecia
Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
description 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.
publishDate 2015
dc.date.none.fl_str_mv 2015-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/46148
Natiello, Mario A.; Solari, Hernan Gustavo; On the removal of infinities from divergent series; University of Exeter. School of Education; Philosophy of Mathematics Education Journal; 29; 7-2015; 1-11
1465-2978
CONICET Digital
CONICET
url http://hdl.handle.net/11336/46148
identifier_str_mv Natiello, Mario A.; Solari, Hernan Gustavo; On the removal of infinities from divergent series; University of Exeter. School of Education; Philosophy of Mathematics Education Journal; 29; 7-2015; 1-11
1465-2978
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/pome29/index.html
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv University of Exeter. School of Education
publisher.none.fl_str_mv University of Exeter. School of Education
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.993085

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