Artículos de revistas
On the removal of infinities from divergent series
Fecha
2015-07Registro en:
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
Autor
Natiello, Mario A.
Solari, Hernan Gustavo
Resumen
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.