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Richard Dedekind information


Richard Dedekind
Born(1831-10-06)6 October 1831
Braunschweig, Duchy of Brunswick
Died12 February 1916(1916-02-12) (aged 84)
Braunschweig, German Empire
NationalityGerman
Alma materCollegium Carolinum
University of Göttingen
Known forDedekind cut
Dedekind-Peano axioms
Abstract algebra
Algebraic number theory
Real numbers
Logicism
Scientific career
FieldsMathematics
Philosophy of mathematics
Doctoral advisorCarl 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.

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Richard Dedekind

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Julius Wilhelm Richard Dedekind [ˈdeːdəˌkɪnt] (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number...

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Dedekind cut

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In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind (but previously considered by Joseph Bertrand), are а method of construction...

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Dedekind domain

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In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors...

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Peano axioms

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provided an axiomatization of natural-number arithmetic. In 1888, Richard Dedekind proposed another axiomatization of natural-number arithmetic, and in 1889...

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Dedekind sum

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this article lists only a small fraction of these. Dedekind sums were introduced by Richard Dedekind in a commentary on fragment XXVIII of Bernhard Riemann's...

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Dedekind eta function

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In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane...

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Dedekind zeta function

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ζK(s) = 0 and 0 < Re(s) < 1, then Re(s) = 1/2. The Dedekind zeta function is named for Richard Dedekind who introduced it in his supplement to Peter Gustav...

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Dedekind number

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mathematics, the Dedekind numbers are a rapidly growing sequence of integers named after Richard Dedekind, who defined them in 1897. The Dedekind number M(n)...

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Number

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Weierstrass (by his pupil E. Kossak), Eduard Heine, Georg Cantor, and Richard Dedekind was brought about. In 1869, Charles Méray had taken the same point...

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Dedekind group

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with all elements of odd order. Dedekind groups are named after Richard Dedekind, who investigated them in (Dedekind 1897), proving a form of the above...

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Modular lattice

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semimodularity. Modular lattices are sometimes called Dedekind lattices after Richard Dedekind, who discovered the modular identity in several motivating...

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Bernhard Riemann

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wissenschaftlicher Nachlass. herausgegeben von Heinrich Weber unter Mitwirkung von Richard Dedekind, Leipzig, B. G. Teubner 1876, 2. Auflage 1892, Nachdruck bei Dover...

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Finite set

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then the following conditions are all equivalent: S is a finite set. (Richard Dedekind) Every one-to-one function from S into itself is onto. Every surjective...

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Set theory

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modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly...

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Naive set theory

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that yielded Russell's paradox, and theories of Giuseppe Peano and Richard Dedekind. The assumption that any property may be used to form a set, without...

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Equinumerosity

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infinity). However, Cantor's ideas were defended by others, for example by Richard Dedekind, and ultimately were largely accepted, strongly supported by David...

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Absolute Infinite

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with the absolute. Cantor also mentioned the idea in his letters to Richard Dedekind (text in square brackets not present in original): A multiplicity [he...

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Natural number

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of definitions was introduced by Charles Sanders Peirce, refined by Richard Dedekind, and further explored by Giuseppe Peano; this approach is now called...

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Cardinality

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infinite sets. In the late 19th century Georg Cantor, Gottlob Frege, Richard Dedekind and others rejected the view that the whole cannot be the same size...

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List of geometers

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(a non-Euclidean geometry) and Riemannian geometry Julius Wilhelm Richard Dedekind (1831–1916) Ludwig Burmester (1840–1927) – theory of linkages Edmund...

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Peter Gustav Lejeune Dirichlet

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into close contact with the new generation of researchers, especially Richard Dedekind and Bernhard Riemann. After moving to Göttingen he was able to obtain...

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List of German mathematicians

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Clavius Stephan Cohn-Vossen Paul Cohn Armin B. Cremers Peter Crüger Richard Dedekind Herbert von Denffer Christopher Deninger Otto Dersch Max Deuring Anton...

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