What does set theory mean?
Definitions for set theory
set the·o·ry
This dictionary definitions page includes all the possible meanings, example usage and translations of the word set theory.
Princeton's WordNet
set theorynoun
the branch of pure mathematics that deals with the nature and relations of sets
Wiktionary
set theorynoun
The mathematical theory of sets.
Wikipedia
Set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The 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 considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of naive set theory. After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox) various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed as a foundational system for the whole of mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Besides its foundational role, set theory also provides the framework to develop a mathematical theory of infinity, and has various applications in computer science (such as in the theory of relational algebra), philosophy and formal semantics. Its foundational appeal, together with its paradoxes, its implications for the concept of infinity and its multiple applications, have made set theory an area of major interest for logicians and philosophers of mathematics. Contemporary research into set theory covers a vast array of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals.
ChatGPT
set theory
Set theory is a branch of mathematical logic that studies sets, which are collections of objects or elements. It is a fundamental theory that serves as a basis for nearly every other part of mathematics. The objects within a set are called its elements or members. It involves various operations like union, intersection, difference, and complement, and concepts such as subsets, power sets, finite and infinite sets, among others.
Wikidata
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.
Matched Categories
Numerology
Chaldean Numerology
The numerical value of set theory in Chaldean Numerology is: 9
Pythagorean Numerology
The numerical value of set theory in Pythagorean Numerology is: 9
Translations for set theory
From our Multilingual Translation Dictionary
- teorie množinCzech
- mængdelæreDanish
- Mengentheorie, MengenlehreGerman
- θεωρία των συνόλωνGreek
- teoría de conjuntosSpanish
- joukko-oppiFinnish
- théorie des ensemblesFrench
- teoiric na dtacar, tacartheoiricIrish
- תורת הקבוצותHebrew
- halmazelméletHungarian
- ensemblo-teorioIdo
- mengjafræðiIcelandic
- insiemistica, teoria degli insiemiItalian
- 集合論Japanese
- 집합론Korean
- ratio coniunctorumLatin
- teori setMalay
- verzamelingenleerDutch
- mengdelæreNorwegian
- teoria mnogościPolish
- teoria dos conjuntos, teoria de conjuntosPortuguese
- теория множествRussian
- теорија скупова, teorija skupovaSerbo-Croatian
- mängdläraSwedish
- ทฤษฎีเซตThai
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"set theory." Definitions.net. STANDS4 LLC, 2024. Web. 15 Jun 2024. <https://www.definitions.net/definition/set+theory>.
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