"Dedekind" redirects here. For other uses, see Dedekind (surname).
Richard Dedekind
Born
(1831-10-06)6 October 1831
Braunschweig, Duchy of Brunswick
Died
12 February 1916(1916-02-12) (aged 84)
Braunschweig, German Empire
Nationality
German
Alma mater
Collegium Carolinum University of Göttingen
Known for
Dedekind cut Dedekind-Peano axioms Abstract algebra Algebraic number theory Real numbers Logicism
Scientific career
Fields
Mathematics Philosophy of mathematics
Doctoral advisor
Carl Friedrich Gauss
Julius Wilhelm Richard Dedekind[ˈdeːdəˌkɪnt] (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number theory, abstract algebra (particularly ring theory), and
the axiomatic foundations of arithmetic. His best known contribution is the definition of real numbers through the notion of Dedekind cut. He is also considered a pioneer in the development of modern set theory and of the philosophy of mathematics known as Logicism.
Julius Wilhelm RichardDedekind [ˈdeːdəˌkɪnt] (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number...
In mathematics, Dedekind cuts, named after German mathematician RichardDedekind (but previously considered by Joseph Bertrand), are а method of construction...
In abstract algebra, a Dedekind domain or Dedekind ring, named after RichardDedekind, is an integral domain in which every nonzero proper ideal factors...
provided an axiomatization of natural-number arithmetic. In 1888, RichardDedekind proposed another axiomatization of natural-number arithmetic, and in 1889...
this article lists only a small fraction of these. Dedekind sums were introduced by RichardDedekind in a commentary on fragment XXVIII of Bernhard Riemann's...
In mathematics, the Dedekind eta function, named after RichardDedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane...
ζK(s) = 0 and 0 < Re(s) < 1, then Re(s) = 1/2. The Dedekind zeta function is named for RichardDedekind who introduced it in his supplement to Peter Gustav...
mathematics, the Dedekind numbers are a rapidly growing sequence of integers named after RichardDedekind, who defined them in 1897. The Dedekind number M(n)...
Weierstrass (by his pupil E. Kossak), Eduard Heine, Georg Cantor, and RichardDedekind was brought about. In 1869, Charles Méray had taken the same point...
with all elements of odd order. Dedekind groups are named after RichardDedekind, who investigated them in (Dedekind 1897), proving a form of the above...
semimodularity. Modular lattices are sometimes called Dedekind lattices after RichardDedekind, who discovered the modular identity in several motivating...
wissenschaftlicher Nachlass. herausgegeben von Heinrich Weber unter Mitwirkung von RichardDedekind, Leipzig, B. G. Teubner 1876, 2. Auflage 1892, Nachdruck bei Dover...
then the following conditions are all equivalent: S is a finite set. (RichardDedekind) Every one-to-one function from S into itself is onto. Every surjective...
modern study of set theory was initiated by the German mathematicians RichardDedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly...
that yielded Russell's paradox, and theories of Giuseppe Peano and RichardDedekind. The assumption that any property may be used to form a set, without...
infinity). However, Cantor's ideas were defended by others, for example by RichardDedekind, and ultimately were largely accepted, strongly supported by David...
with the absolute. Cantor also mentioned the idea in his letters to RichardDedekind (text in square brackets not present in original): A multiplicity [he...
of definitions was introduced by Charles Sanders Peirce, refined by RichardDedekind, and further explored by Giuseppe Peano; this approach is now called...
infinite sets. In the late 19th century Georg Cantor, Gottlob Frege, RichardDedekind and others rejected the view that the whole cannot be the same size...
(a non-Euclidean geometry) and Riemannian geometry Julius Wilhelm RichardDedekind (1831–1916) Ludwig Burmester (1840–1927) – theory of linkages Edmund...
into close contact with the new generation of researchers, especially RichardDedekind and Bernhard Riemann. After moving to Göttingen he was able to obtain...
Clavius Stephan Cohn-Vossen Paul Cohn Armin B. Cremers Peter Crüger RichardDedekind Herbert von Denffer Christopher Deninger Otto Dersch Max Deuring Anton...