ON THE REMOVAL OF INFINITIES FROM DIVERGENT SERIES

M A NATIELLO; H G SOLARI

Philosophy of Mathematics Education Journal

University of Exeter, United Kingdom.

Lugar: Exewter; Año: 2015 vol. 29

p { margin-bottom: 0.25cm; direction: ltr; color: rgb(0, 0, 10); line-height: 120%; text-align: left; }p.western { }a:link { }Theconsequences of adopting other definitions of the concepts of sum andconvergence of a series are discussed in the light of historical andepistemological contexts. We show that some divergent seriesappearing in the context of renormalization methods cannot beassigned finite values while preserving a minimum of consistency withstandard summation, without at the same time obtainingcontradictions, thus destroying the mathematical building (theconditions are known as Hardy?s axioms). We finally discuss theepistemological costs of accepting these practices in the name ofinstrumentalism.