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51 relations: Abraham Robinson, Adviser, Alain Connes, American Mathematical Monthly, Archive for History of Exact Sciences, Axiom of choice, Bulletin of the American Mathematical Society, Conservative extension, Constructive non-standard analysis, Constructivism (mathematics), Das Kapital, David Tall, Dixmier trace, Donald A. Gillies, Economics, Edward Nelson, Elementary Calculus: An Infinitesimal Approach, Errett Bishop, Foundations of Science, Geoffrey Hellman, Henk J. M. Bos, Howard Jerome Keisler, Hyperreal number, Ian Stewart (mathematician), Influence of non-standard analysis, Intellectica, Internal set theory, Invariant subspace problem, Joseph Dauben, Law of excluded middle, Margaret Thatcher, Martin Davis, Non-standard analysis, Non-standard calculus, Paul Halmos, Philip J. Davis, Quantum mechanics, Revolutions in Mathematics, Robert M. Solovay, Saharon Shelah, Semën Samsonovich Kutateladze, Smooth infinitesimal analysis, Teetotalism, Terence Tao, The Mathematics Enthusiast, Thermodynamics, Vadim Komkov, Vladimir Kanovei, Wilhelmus Luxemburg, Zermelo–Fraenkel set theory, ..., (ε, δ)-definition of limit. Expand index (1 more) »
Abraham Robinson
Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics.
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Adviser
An adviser or advisor is normally a person with more and deeper knowledge in a specific area and usually also includes persons with cross-functional and multidisciplinary expertise.
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Alain Connes
Alain Connes (born 1 April 1947) is a French mathematician, currently Professor at the Collège de France, IHÉS, Ohio State University and Vanderbilt University.
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American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
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Archive for History of Exact Sciences
Archive for History of Exact Sciences is a peer-reviewed academic journal published quarterly by Springer Science+Business Media, covering the history of mathematics and of astronomy observations and techniques, epistemology of science, and philosophy of science from Antiquity until now.
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Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.
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Bulletin of the American Mathematical Society
The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.
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Conservative extension
In mathematical logic, a conservative extension is a supertheory of a theory which is often convenient for proving theorems, but proves no new theorems about the language of the original theory.
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Constructive non-standard analysis
In mathematics, constructive nonstandard analysis is a version of Abraham Robinson's non-standard analysis, developed by Moerdijk (1995), Palmgren (1998), Ruokolainen (2004).
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Constructivism (mathematics)
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists.
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Das Kapital
Das Kapital, also known as Capital.
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David Tall
David Orme Tall (born 15 May 1941) is Emeritus Professor in Mathematical Thinking at the University of Warwick.
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Dixmier trace
In mathematics, the Dixmier trace, introduced by, is a non-normal trace on a space of linear operators on a Hilbert space larger than the space of trace class operators.
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Donald A. Gillies
Donald A. Gillies (born 1944) is a British philosopher and historian of science and mathematics.
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Economics
Economics is the social science that studies the production, distribution, and consumption of goods and services.
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Edward Nelson
Edward Nelson (May 4, 1932 – September 10, 2014) was a professor in the Mathematics Department at Princeton University.
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Elementary Calculus: An Infinitesimal Approach
Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler.
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Errett Bishop
Errett Albert Bishop (July 14, 1928 – April 14, 1983) was an American mathematician known for his work on analysis.
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Foundations of Science
Foundations of Science is a peer-reviewed interdisciplinary academic journal focussing on methodological and philosophical topics concerning the structure and the growth of science.
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Geoffrey Hellman
Geoffrey Hellman is an American professor and philosopher.
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Henk J. M. Bos
Hendrik Jan Maarten "Henk" Bos (born 17 July 1940, Enschede) is a Dutch historian of mathematics.
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Howard Jerome Keisler
Howard Jerome Keisler (born 3 December 1936) is an American mathematician, currently professor emeritus at University of Wisconsin–Madison.
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Hyperreal number
The system of hyperreal numbers is a way of treating infinite and infinitesimal quantities.
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Ian Stewart (mathematician)
Ian Nicholas Stewart (born 24 September 1945) is a British mathematician and a popular-science and science-fiction writer.
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Influence of non-standard analysis
The influence of Abraham Robinson's theory of non-standard analysis has been felt in a number of fields.
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Intellectica
Intellectica is a biannual peer-reviewed academic journal of cognitive psychology that was established in 1985 and covers research in a broad range of subjects such as perception, motricity, language, and reasoning.
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Internal set theory
Internal set theory (IST) is a mathematical theory of sets developed by Edward Nelson that provides an axiomatic basis for a portion of the non-standard analysis introduced by Abraham Robinson.
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Invariant subspace problem
In the field of mathematics known as functional analysis, the invariant subspace problem is a partially unresolved problem asking whether every bounded operator on a complex Banach space sends some non-trivial closed subspace to itself.
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Joseph Dauben
Joseph Warren Dauben (born 29 December 1944, Santa Monica) is a Herbert H. Lehman Distinguished Professor of History at the Graduate Center of the City University of New York.
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Law of excluded middle
In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is true or its negation is true.
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Margaret Thatcher
Margaret Hilda Thatcher, Baroness Thatcher, (13 October 19258 April 2013) was a British stateswoman who served as Prime Minister of the United Kingdom from 1979 to 1990 and Leader of the Conservative Party from 1975 to 1990.
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Martin Davis
Martin David Davis (born March 8, 1928) is an American mathematician, known for his work on Hilbert's tenth problem.
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Non-standard analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.
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Non-standard calculus
In mathematics, non-standard calculus is the modern application of infinitesimals, in the sense of non-standard analysis, to differential and integral calculus.
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Paul Halmos
Paul Richard Halmos (Halmos Pál; March 3, 1916 – October 2, 2006) was a Hungarian-Jewish-born American mathematician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces).
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Philip J. Davis
Philip J. Davis (January 2, 1923 – March 13, 2018) was an American academic applied mathematician.
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Revolutions in Mathematics
Revolutions in Mathematics is a collection of essays in the history and philosophy of mathematics.
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Robert M. Solovay
Robert Martin Solovay (born December 15, 1938) is an American mathematician specializing in set theory.
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Saharon Shelah
Saharon Shelah (שהרן שלח) is an Israeli mathematician.
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Semën Samsonovich Kutateladze
Semën Samsonovich Kutateladze (born October 2, 1945 in Leningrad, now St. Petersburg) is a mathematician.
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Smooth infinitesimal analysis
Smooth infinitesimal analysis is a modern reformulation of the calculus in terms of infinitesimals.
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Teetotalism
Teetotalism is the practice or promotion of complete personal abstinence from alcoholic beverages.
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Terence Tao
Terence Chi-Shen Tao (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics.
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The Mathematics Enthusiast
The Mathematics Enthusiast is a triannual peer-reviewed open access academic journal covering undergraduate mathematics, mathematics education, including historical, philosophical, and cross-cultural perspectives on mathematics.
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Thermodynamics
Thermodynamics is the branch of physics concerned with heat and temperature and their relation to energy and work.
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Vadim Komkov
Vadim Komkov (August 18, 1919 – May 14, 2008) was born in Moscow, Russia, and raised in Poland after his parents died in the Bolshevik Revolution.
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Vladimir Kanovei
Vladimir G. Kanovei (born 1951) is a Russian mathematician working at the Institute for Information Transmission Problems in Moscow, Russia.
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Wilhelmus Luxemburg
Wilhelmus Anthonius Josephus Luxemburg (born 11 April 1929, in Delft, Netherlands) is Professor of Mathematics, Emeritus at the California Institute of Technology.
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Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
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(ε, δ)-definition of limit
In calculus, the (ε, δ)-definition of limit ("epsilon–delta definition of limit") is a formalization of the notion of limit.
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Redirects here:
Bishop-Keisler controversy, Bishop-Kiesler, Bishop–Keisler controversy, Criticism of nonstandard analysis.
References
[1] https://en.wikipedia.org/wiki/Criticism_of_non-standard_analysis
