Searches , social queries for RICHARD DEDEKIND
Search references for RICHARD DEDEKIND. Phrases containing RICHARD DEDEKIND
See searches and references containing RICHARD DEDEKIND!
Search references for RICHARD DEDEKIND. Phrases containing RICHARD DEDEKIND
See searches and references containing RICHARD DEDEKIND!RICHARD DEDEKIND
German mathematician (1831–1916)
Julius Wilhelm Richard Dedekind (/ˈdeɪdɪkɪnd/; German: [ˈdeːdəˌkɪnt]; 6 October 1831 – 12 February 1916) was a German mathematician who made important
Richard_Dedekind
Method of construction of the real numbers
In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind (but previously considered by Joseph Bertrand), are а method of constructing
Dedekind_cut
Mathematical function
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
Dedekind_eta_function
Set with an equinumerous proper subset
In mathematics, a set A is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset B of A is equinumerous to A
Dedekind-infinite_set
Theorem in algebraic number theory
the Dedekind–Kummer theorem describes how a prime ideal in a Dedekind domain factors over the domain's integral closure. It is named after Richard Dedekind
Dedekind–Kummer_theorem
Axioms for the natural numbers
provided an axiomatization of natural-number arithmetic. In 1888, Richard Dedekind proposed another axiomatization of natural-number arithmetic, and in 1889
Peano_axioms
Smallest complete lattice containing a partial order
and constructed it, and after Richard Dedekind because its construction generalizes the Dedekind cuts used by Dedekind to construct the real numbers from
Dedekind–MacNeille_completion
Branch of mathematics that studies sets
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
Set_theory
Combinatorial sequence of numbers
mathematics, the Dedekind numbers are a rapidly growing sequence of integers named after Richard Dedekind, who defined them in 1897. The Dedekind number M (
Dedekind_number
Algebraic structure with addition and multiplication
contributions by Richard Dedekind, David Hilbert, Abraham Fraenkel, and Emmy Noether. Rings were first formalized as a generalization of Dedekind domains that
Ring_(mathematics)
Algebra with unique prime factorization
In mathematics, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into
Dedekind_domain
German mathematician (1826–1866)
wissenschaftlicher Nachlass. herausgegeben von Heinrich Weber unter Mitwirkung von Richard Dedekind, Leipzig, B. G. Teubner 1876, 2. Auflage 1892, Nachdruck bei Dover
Bernhard_Riemann
Group whose subgroups are all normal
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
Dedekind_group
Surname list
swimmer and goalball player Richard Dedekind (1831–1916), German mathematician 19293 Dedekind, asteroid named after Richard Dedekind This page lists people
Dedekind_(surname)
German mathematician (1805–1859)
into close contact with the new generation of researchers, especially Richard Dedekind and Bernhard Riemann. After moving to Göttingen he was able to obtain
Peter Gustav Lejeune Dirichlet
Peter_Gustav_Lejeune_Dirichlet
Cantor–Dedekind axiom Dedekind completeness Dedekind cut Dedekind discriminant theorem Dedekind domain Dedekind eta function Dedekind function Dedekind group
List of things named after Richard Dedekind
List_of_things_named_after_Richard_Dedekind
Generalization of the Riemann zeta function for algebraic number fields
equation. Values of Dedekind zeta functions encode important arithmetic data of K. The Dedekind zeta function is named for Richard Dedekind, who introduced
Dedekind_zeta_function
Mathematician (1845–1918)
mountains, Cantor spent much time in mathematical discussions with Richard Dedekind, whom he had met two years earlier while on holiday in Gersau in Switzerland
Georg_Cantor
Mathematician and philosopher (1906–1978)
the foundations of mathematics), building on earlier work by Frege, Richard Dedekind, and Georg Cantor. Gödel's discoveries in the foundations of mathematics
Kurt_Gödel
Basic framework of mathematics
involved. His method anticipated that of Dedekind cuts in the modern definition of real numbers by Richard Dedekind (1831–1916); see Eudoxus of Cnidus § Eudoxus'
Foundations_of_mathematics
Meromorphic function on the complex plane
function). Most notably, the mathematicians Bernhard Riemann (1826–1866), Richard Dedekind (1831–1916), Erich Hecke (1887–1947) and Emil Artin (1898–1962) investigated
L-function
Type of lattice in mathematical order theory
semimodularity. Modular lattices are sometimes called Dedekind lattices after Richard Dedekind, who discovered the modular identity in several motivating
Modular_lattice
data for prime ideals of the ring of integers. It was introduced by Richard Dedekind in 1882. If OK is the ring of integers of K, and tr denotes the field
Different_ideal
Mathematical concept
from works by Cantor, Gottlob Frege, Richard Dedekind and others—using the idea of collections or sets. Dedekind's approach was essentially to adopt the
Infinity
Informal set theories
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
Naive_set_theory
Paradox in set theory
lead to a contradiction (to Cantor's theorem), as he told Hilbert and Richard Dedekind by letter. Hilbert also formulated his own paradox, which relied on
Russell's_paradox
Book by Bertrand Russell
reference. It reported on developments by Giuseppe Peano, Mario Pieri, Richard Dedekind, Georg Cantor, and others. In 1905 Louis Couturat published a partial
The_Principles_of_Mathematics
First article on transfinite set theory
whether or not this proof is constructive. Cantor's correspondence with Richard Dedekind shows the development of his ideas and reveals that he had a choice
Cantor's first set theory article
Cantor's_first_set_theory_article
Algorithm for computing greatest common divisors
extended by Richard Dedekind, who used Euclid's algorithm to study algebraic integers, a new general type of number. For example, Dedekind was the first
Euclidean_algorithm
Concept in philosophy and set theory
his theory of the transfinite. Later, writing to David Hilbert and Richard Dedekind in 1897 and 1899 respectively, Cantor described a paradox similar to
Absolute_infinite
Algebraic structure with addition, multiplication, and division
conceived neither an explicit notion of a field, nor of a group. In 1871 Richard Dedekind introduced, for a set of real or complex numbers that is closed under
Field_(mathematics)
Condition under which an odd prime is a sum of two squares
K^{2}\equiv -1{\pmod {p}}\iff p\equiv 1{\pmod {4}}} , as required. Richard Dedekind gave at least two proofs of Fermat's theorem on sums of two squares
Fermat's theorem on sums of two squares
Fermat's_theorem_on_sums_of_two_squares
Several textbooks of number theory
The best known was written by Peter Gustav Lejeune Dirichlet and Richard Dedekind, and published in 1863. Others were written by Leopold Kronecker, Edmund
Vorlesungen über Zahlentheorie
Vorlesungen_über_Zahlentheorie
Clavius Stephan Cohn-Vossen Paul Cohn Armin B. Cremers Peter Crüger Richard Dedekind Herbert von Denffer Christopher Deninger Otto Dersch Max Deuring Anton
List_of_German_mathematicians
Branch of mathematics
to finite fields with p n {\displaystyle p^{n}} elements. In 1871 Richard Dedekind introduced, for a set of real or complex numbers that is closed under
Abstract_algebra
Italian mathematician (1853–1925)
of real numbers, an area in which he extended the research begun by Richard Dedekind. Completing his high school studies privately at only 16 years of age
Gregorio_Ricci-Curbastro
Finite ordered list of elements
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Tuple
Set with exactly one element
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Singleton_(mathematics)
Arithmetical function
is the empty product, has value 1.) The function was introduced by Richard Dedekind in connection with modular functions. The value of ψ ( n ) {\displaystyle
Dedekind_psi_function
(a non-Euclidean geometry) and Riemannian geometry Julius Wilhelm Richard Dedekind (1831–1916) Ludwig Burmester (1840–1927) – theory of linkages Edmund
List_of_geometers
School of thought in philosophy of mathematics
initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano. Dedekind's path to logicism had a turning point when he was able
Logicism
German polymath and scholar (1777–1855)
preferring to focus on his own work, some of his students, such as Richard Dedekind and Bernhard Riemann, became well-known and influential mathematicians
Carl_Friedrich_Gauss
first stated as a conjecture in a letter of 1896 by the mathematician Richard Dedekind to F. G. Frobenius, who proved it by methods which began a new branch
Frobenius_determinant_theorem
Process of repeating items in a self-similar way
postulates or Dedekind–Peano axioms), are axioms for the natural numbers presented in the 19th century by the German mathematician Richard Dedekind and by the
Recursion
Czech mathematician
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Thomas_Jech
Branch of number theory
mathematicians including Ernst Kummer, Peter Gustav Lejeune Dirichlet and Richard Dedekind. Many of the annotations given by Gauss are in effect announcements
Algebraic_number_theory
Standard system of axiomatic set theory
The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. However, the discovery of paradoxes in naive set theory
Zermelo–Fraenkel_set_theory
paradoxes of enumeration. "I see it but I don't believe," Cantor wrote to Richard Dedekind after proving that the set of points of a square has the same cardinality
Paradoxes_of_set_theory
Pair of logical equivalences
ISBN 978-1-285-19654-1 Moore, Brooke Noel (2012). Critical thinking. Richard Parker (10th ed.). New York: McGraw-Hill. ISBN 978-0-07-803828-0. OCLC 689858599
De_Morgan's_laws
Degrees of separation from Paul Erdős
Erdős number is either Antoine Lavoisier (born 1743, Erdős number 13), Richard Dedekind (born 1831, Erdős number 7), or Ferdinand Georg Frobenius (born 1849
Erdős_number
Number that is not a ratio of integers
Eduard Heine (Crelle's Journal, 74), Georg Cantor (Annalen, 5), and Richard Dedekind. Méray had taken in 1869 the same point of departure as Heine, but
Irrational_number
Number representing a continuous quantity
need for a rigorous definition of the real numbers. Beginning with Richard Dedekind in 1858, several mathematicians worked on the definition of the real
Real_number
Theorem relating a group with the image and kernel of a homomorphism
for vector spaces, modules, and rings. It dates back to the work of Richard Dedekind, and was further formalized by Emmy Noether into the isomorphism theorems
Fundamental theorem on homomorphisms
Fundamental_theorem_on_homomorphisms
Mathematical set with repetitions allowed
more detail in 1685. Multisets appeared explicitly in the work of Richard Dedekind. Other mathematicians formalized multisets and began to study them
Multiset
3-volume treatise on mathematics, 1910–1913
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Principia_Mathematica
System of mathematical set theory
says he wants to show how the original theory of Georg Cantor and Richard Dedekind can be reduced to a few definitions and seven principles or axioms
Zermelo_set_theory
therefore be a Euclidean domain. The notion of a Dedekind–Hasse norm was developed independently by Richard Dedekind and, later, by Helmut Hasse. They both noticed
Dedekind–Hasse_norm
Concept in mathematics
application of ACω, here is a proof (from ZF + ACω) that every infinite set is Dedekind-infinite: Let X {\displaystyle X} be infinite. For each natural number
Axiom_of_countable_choice
Problem in set theory
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Suslin's_problem
Used to count, measure, and label
Weierstrass (1872), Eduard Heine (1872), Georg Cantor (1883), and Richard Dedekind (1872). A transcendental number is a numerical value that is not the
Number
Paradox in set theory
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Burali-Forti_paradox
Mathematical connection between field theory and group theory
ISBN 978-0-486-45868-7. Scharlau, Winfried; Dedekind, Ilse; Dedekind, Richard (1981). Richard Dedekind 1831–1981; eine Würdigung zu seinem 150. Geburtstag
Galois_theory
historical reasons. The first three, due to Georg Cantor/Charles Méray, Richard Dedekind/Joseph Bertrand and Karl Weierstrass all occurred within a few years
Construction of the real numbers
Construction_of_the_real_numbers
Elements in exactly one of two sets
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Symmetric_difference
Set whose pairs have minima and maxima
1007/s11229-009-9667-9. S2CID 11012081. Summary of the history of lattices. Dedekind, Richard (1897), "Über Zerlegungen von Zahlen durch ihre grössten gemeinsamen
Lattice_(order)
Mathematical concept
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Equivalence_class
Proof in set theory
thereof. Various models have been studied, such as the Cauchy reals or the Dedekind reals, among others. The former relate to quotients of sequences while
Cantor's_diagonal_argument
Mathematical term; concerning axioms used to derive theorems
assumed. 1888 Richard Dedekind construction of the real numbers When Dedekind introduced his construction of real numbers by Dedekind cuts, axioms for
Axiomatic_system
Algebraic integer which represents an ideal in a ring of integers
number field; the idea was developed by Ernst Kummer, and led to Richard Dedekind's definition of ideals for rings. An ideal in the ring of integers of
Ideal_number
Measure of the size of the ring of integers
polynomial x 3 − x 2 − 2 x − 8 {\displaystyle x^{3}-x^{2}-2x-8} . This is Richard Dedekind's original example of a number field whose ring of integers does not
Discriminant of an algebraic number field
Discriminant_of_an_algebraic_number_field
Topics referred to by the same term
theory, Dedekind function can refer to any of three functions, all introduced by Richard Dedekind Dedekind eta function Dedekind psi function Dedekind zeta
Dedekind_function
Collection of mathematical objects
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Set_(mathematics)
Theorem in set theory
omitted because his proof turned out to be flawed while the name of Richard Dedekind, who first proved it, is not connected with the theorem. According
Schröder–Bernstein_theorem
Concept in axiomatic set theory
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Axiom_schema_of_specification
Finite extension of the rationals
a Dedekind ring (or Dedekind domain), in honor of Richard Dedekind, who undertook a deep study of rings of algebraic integers. For general Dedekind rings
Algebraic_number_field
Diagram that shows all possible logical relations between a collection of sets
Willum; Manalo, Emmanuel; Viana, Petrucio; Bhattacharjee, Reetu; Burns, Richard (eds.). Diagrammatic Representation and Inference. Lecture Notes in Computer
Venn_diagram
Set whose elements all belong to another set
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Subset
Orientation-preserving mapping class group of the torus
print in (Klein & 1878/79a), where it is credited to Richard Dedekind, in reference to (Dedekind 1877). The map of groups (2, 3, ∞) → (2, 3, n) (from
Modular_group
Branch of mathematics
are of great importance. Moreover, works of Charles Sanders Peirce, Richard Dedekind, and Ernst Schröder also consider concepts of order theory. Contributors
Order_theory
Any one of the distinct objects that make up a set in set theory
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Element_of_a_set
Arithmetic operation
This definition was first published, in a slightly modified form, by Richard Dedekind in 1872. The commutativity and associativity of real addition are immediate;
Addition
Swiss mathematician (1707–1783)
Charles Coulston (ed.). Dictionary of Scientific Biography. Vol. 4: Richard Dedekind – Firmicus Maternus. New York: Charles Scribner's Sons. pp. 467–484
Leonhard_Euler
Size of a possibly infinite set
or |Y| ≤ |X|. A set X is called Dedekind-infinite if there exists a proper subset Y of X with |X| = |Y|, and Dedekind-finite if such a subset does not
Cardinal_number
American philosopher and logician (1908–2000)
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Willard_Van_Orman_Quine
Mathematical set containing no elements
Journal of Philosophy 91: 430–49. Reprinted in 1998, Logic, Logic and Logic (Richard Jeffrey, and Burgess, J., eds.) Harvard University Press, 54–72. Halmos
Empty_set
American mathematician (1934–2007)
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Paul_Cohen
English philosopher and logician (1872–1970)
from the original on 17 October 2018. Retrieved 27 December 2008. Rempel, Richard (1979). "From Imperialism to Free Trade: Couturat, Halevy and Russell's
Bertrand_Russell
Form of mathematical proof
Boole, Augustus De Morgan, Charles Sanders Peirce, Giuseppe Peano, and Richard Dedekind. The simplest and most common form of mathematical induction infers
Mathematical_induction
Finite collection of distinct objects
finite set. (Richard Dedekind) Every one-to-one function from S {\displaystyle S} into itself is onto. A set with this property is called Dedekind-finite.
Finite_set
Submodule of a mathematical ring
with "ideal" objects in geometry such as points at infinity. In 1876, Richard Dedekind replaced Kummer's undefined concept by concrete sets of numbers, sets
Ideal_(ring_theory)
Term in set theory
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Almost
Set that is not a finite set
a set is infinite if and only if the power set of its power set is a Dedekind-infinite set, having a proper subset equinumerous to itself. If the axiom
Infinite_set
Number measuring the chance an event occurs
Sylvestre Lacroix (1816), Littrow (1833), Adolphe Quetelet (1853), Richard Dedekind (1860), Helmert (1872), Hermann Laurent (1873), Liagre, Didion and
Probability
Basic notion of sameness in mathematics
they satisfy membership, sets are extentional. José Ferreirós credits Richard Dedekind for being the first to explicitly state the principle, although he
Equality_(mathematics)
In mathematics, Dedekind sums are certain finite sums of products of a sawtooth function. Dedekind introduced them in the 1880's to express the functional
Dedekind_sum
Decomposition of periodic functions
zu Göttingen, vol. 13, 1867. Published posthumously for Riemann by Richard Dedekind (in German). Archived from the original on 20 May 2008. Retrieved 19
Fourier_series
Number used for counting
1888, Richard Dedekind proposed another axiomatization of natural-number arithmetic, and in 1889, Peano published a simplified version of Dedekind's axioms
Natural_number
City and urban agglomeration in Lower Saxony, Germany
notable pupils, such as Carl Friedrich Gauss, Hoffmann von Fallersleben, Richard Dedekind and Louis Spohr. Since 2004, Braunschweig also has an International
Braunschweig
Set of the elements not in a given subset
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Complement_(set_theory)
Set of elements common to all of some sets
Burali-Forti paradox Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine
Intersection_(set_theory)
travel, tourism, insurance
RICHARD DEDEKIND
RICHARD DEDEKIND
Boy/Male
Christian & English(British/American/Australian)
Powerful Ruler
Male
Scandinavian
Scandinavian form of Old High German Ricohard, RIKARD means "powerful ruler."
Male
French
Norman French form of Latin Ricardus, RICHAUD means "powerful ruler."
Surname or Lastname
English and French
English and French : variant of Richard.A Ricard is documented in Montreal in 1665, with the secondary surname Saint-Germain.
Male
Slovene
Slovene form of Old High German Ricohard, RIHARD means "powerful ruler."
Male
Italian
Italian form of Latin Ricardus, RICCARDO means "powerful ruler."
Surname or Lastname
English
English : patronymic from Rickard.
Female
Italian
Feminine form of Italian Riccardo, RICCARDA means "powerful ruler."
Boy/Male
Teutonic American English Shakespearean French German
Powerful ruler.
Male
Spanish
Spanish form of Latin Ricardus, RICARDO means "powerful ruler."
Male
Finnish
Finnish form of Old High German Ricohard, RIKHARD means "powerful ruler."
Surname or Lastname
English
English : variant of Richard.
Surname or Lastname
English (Devon and Cornwall) and German
English (Devon and Cornwall) and German : variant of Richard.Americanized spelling of German Reichardt.
Boy/Male
American, Anglo, Arabic, Australian, Bengali, British, Chinese, Christian, Czechoslovakian, Danish, Dutch, English, French, German, Irish, Italian, Jamaican, Netherlands, Swedish, Swiss, Teutonic
Brave One; Strong Ruler; A Teutonic Name from the European Middle Ages; Dominant Ruler; Powerful Leader
Female
Spanish
Feminine form of Spanish Ricardo, RICARDA means "powerful ruler." Used mostly in Germany.
Male
German
Contracted form of German Reginhard, REINHARD means "wise and strong."
Female
English
Feminine form of English Richard, RICHARDA means "powerful ruler."
Surname or Lastname
English, French, German, and Dutch
English, French, German, and Dutch : from a Germanic personal name
composed of the elements rīc ‘power(ful)’ + hard
‘hardy’, ‘brave’, ‘strong’.A Richard from Normandy is documented in Quebec City in 1669, with
the secondary surname
Surname or Lastname
English and German
English and German : patronymic from the personal name Richard. Richards is a frequent name in Wales.
Male
English
English form of Norman French Richaud, RICHARD means "powerful ruler."
RICHARD DEDEKIND
RICHARD DEDEKIND
RICHARD DEDEKIND
RICHARD DEDEKIND
RICHARD DEDEKIND
RICHARD DEDEKIND
RICHARD DEDEKIND
travel, tourism, insurance