E. H. Dirksen's contributions to the foundation of analysis
type: Item
instance of: scholarly article
title: E. H. Dirksen's contributions to the foundation of analysis
zbMATH Open document ID: 1033.01019
DOI: 10.1007/BF02908590
author: Gert Schubring
published in: NTM. Neue Serie
publication date: 2003-09-14T00:00:00Z
review text: Enno Heeren Dirksen (1788--1850) was a full professor of mathematics at Berlin University since 1824 and in several respects a transitionary figure. The author gives information on one little known contribution by Dirksen to introduce rigour into the foundations of analysis. His review (1829) of Cauchy's \textit{Cours d'Analyse} showed a gap in Cauchy's alleged proof that the limit function of a series of continuous functions is continuous. Schubring explains that Dirksen introduced some new notation that made it easier to express double (iterated) limits. He argues that in this Dirksen went even further than Abel who introduced a counterexample to Cauchy's theorem. However, Dirksen was stronger as a critic than as a constructive mathematician and did not introduce uniform convergence.
reviewed by: Reinhard Siegmund-Schultze
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A70
zbMATH DE Number: 1925619
zbMATH Keywords: E. H. Dirksen
zbMATH Keywords: Cauchy
zbMATH Keywords: iterated and uniform convergence
MaRDI profile type: Publication
cites work: Q5675328
cites work: Q4284037
cites work: Q3026957
cites work: Q4861001
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description: scientific article; zbMATH DE number 1925619