nLab Richard Dedekind

• Wikipedia entry

• SEP, Dedekind’s Contributions to the Foundations of Mathematics

Selected writings

In which the notion of a field was first introduced, but only for subfields of the complex numbers:

• Gustav Lejeune Dirichlet (1871), Richard Dedekind (ed.), Vorlesungen über Zahlentheorie (Lectures on Number Theory) (in German), vol. 1 (2nd ed.), Braunschweig, Germany: Friedrich Vieweg und Sohn (Google Books)

Introducing the notion of Dedekind cuts for the definition of the real numbers:

• Richard Dedekind, Stetigkeit und irrationale Zahlen (1872) [Google Books, retyped: web]

• Richard Dedekind (transl. by W. Beman), Continuity and irrational numbers, Chapter I in: Essays on the Theory of Numbers, Chicago (1901) [Project Gutenberg, pdf]

On axioms for the natural numbers and infinite sets:

• Richard Dedekind, Was sind und was sollen die Zahlen? (1888) [scan: pdf, doi:10.1007/978-3-663-02788-1]

• Richard Dedekind (transl. by W. Beman), The nature and meaning of numbers, Chapter II in: Essays on the Theory of Numbers, Chicago (1901) [Project Gutenberg, pdf]

These two essays contain the definitions of Dedekind cuts and infinite sets (this definition is now taken to define Dedekind infinite sets) an axiomatization of the natural numbers adapted by Peano into Peano arithmetic (Dedekind-Peano axioms).

category: people