A noun is a type of word the meaning of which determines reality. Nouns provide the names for all things: people, objects, sensations, feelings, etc.
WHAT DOES SET THEORY MEAN IN ENGLISH?
Set theory
Set theory is the branch of mathematical logic that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects. The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known. Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community. Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals.
Definition of set theory in the English dictionary
The definition of set theory in the dictionary is the branch of mathematics concerned with the properties and interrelationships of sets. Other definition of set theory is a theory constructed within first-order logic that yields the mathematical theory of classes, esp one that distinguishes sets from proper classes as a means of avoiding certain paradoxes.
Synonyms and antonyms of set theory in the English dictionary of synonyms
SYNONYMS
WORDS RELATING TO «SET THEORY»
set theorybasictheoryexamplesproblemsproofsmathsymbolsmusicbranchmathematicallogicthatstudiessetswhichcollectionsobjectsalthoughtypeobjectcollectedintoappliedmostoftenrelevantmathematicslanguageusedmenuvenndiagramsintroductionintervalsbuildernotationpointslocuscommonnumberclosurehistoryratherdifferentfromotherareaslongprocessusuallytracedwikibooksopenbooksworldconcernedconceptessentiallycollectioncallelementsbecausegeneralityformsencyclopediabritannicadealspropertieswelldefinednaturesuchxkcdprevrandomnextpermanentlinkthiscomichttpimageuniversitytorontothesenotesgraduatecoursetheircomingfundamentalsmathematiciansstanfordphilosophyscienceinfiniteabstractpervadewholethomasjechamazonshippingqualifyingoffersmonographcoversrecentmajoradvancesvariouswhatchristianfundamentalistshave
The translations of set theory from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «set theory» in English.
List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «set theory».
FREQUENCY OF USE OF THE TERM «SET THEORY» OVER TIME
The graph expresses the annual evolution of the frequency of use of the word «set theory» during the past 500 years. Its implementation is based on analysing how often the term «set theory» appears in digitalised printed sources in English between the year 1500 and the present day.
Examples of use in the English literature, quotes and news about set theory
EXAMPLES
2 QUOTES WITH «SET THEORY»
Famous quotes and sentences with the word set theory.
1
Harrison Birtwistle
Minimalism now is a reaction to what came before. It's absolutely of its time. Music moved into the set theory thing, and moved out of it.
2
Harrison Birtwistle
When I dealt with set theory, I could never make it be the music that I wanted.
10 ENGLISH BOOKS RELATING TO «SET THEORY»
Discover the use of set theory in the following bibliographical selection. Books relating to set theory and brief extracts from same to provide context of its use in English literature.
1
Naive SetTheory
The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics." --PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH
P. R. Halmos, 1960
2
Elements of SetTheory
This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Herbert B. Enderton, 1977
3
SetTheory
This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.
Andras Hajnal, Peter Hamburger, 1999
4
Fuzzy SetTheory—and Its Applications
Since its inception, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines.
Hans-Jürgen Zimmermann, 2001
5
SetTheory and Metric Spaces
This is a book that could profitably be read by many graduate students or by seniors in strong major programs ... has a number of good features.
Irving Kaplansky, 2001
6
Discovering Modern SetTheory: The basics
Recommended. --Monatshefte fur Mathematik This book is an introduction to set theory for beginning graduate students who want to get a sound grounding in those aspects of set theory used extensively throughout other areas of mathematics.
Winfried Just, Martin Weese, 1996
7
SetTheory: An Introduction
A text on set theory that includes solutions to the problems.
Robert L. Vaught, 2001
8
Axiomatic SetTheory
Since the first edition of this book was published, Paul J. Cohen has shown that
the axiom of choice is independent of the other axioms of Zermelo-Fraenkel settheory. Godel proved earlier that if Zermelo-Fraenkel's set theory is consistent, ...
Patrick Suppes, 2012
9
Basic SetTheory
This book provides just that in the form of a leisurely exposition for a diversified audience.
Nikolai Konstantinovich Vereshchagin, Alexander Shen, 2002
10
Algebraic SetTheory
This book offers a new algebraic approach to set theory.
Andri Joyal, Ieke Moerdijk, 1995
3 NEWS ITEMS WHICH INCLUDE THE TERM «SET THEORY»
Find out what the national and international press are talking about and how the term set theory is used in the context of the following news items.
1
Will Computers Redefine the Roots of Math?
Set theory grew out of an impulse to put mathematics on an entirely rigorous footing—a logical basis even more secure than numbers themselves. Set theory ... «Wired, Jun 15»
2
How Infinitely Big Is God?
You can use Set Theory to study the cereal aisle at a grocery store. What cereal boxes have a cartoon character on them (Set A)? What cereals will Mom let me ... «ChristianityToday.com, Dec 14»
3
Russell's Paradox: Here's Why Math Can't Have A Set Of Everything
The people who invented set theory also started out with a pretty vague idea of what sets are, and this vagueness led to some serious problems. Mathematician ... «Business Insider, Nov 13»
REFERENCE
« EDUCALINGO. Set theory [online]. Available <https://educalingo.com/en/dic-en/set-theory>. Apr 2024 ».
