Definitions for set theory
set the·o·ry

Princeton's WordNetRate this definition:0.0 / 0 votes

1. set theorynoun

   the branch of pure mathematics that deals with the nature and relations of sets

WiktionaryRate this definition:0.0 / 0 votes

1. set theorynoun

   The mathematical theory of sets.

WikipediaRate this definition:0.0 / 0 votes

1. 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.

ChatGPTRate this definition:0.0 / 0 votes

1. 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.

WikidataRate this definition:0.0 / 0 votes

1. 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

1. • Mathematics
   • Pure Mathematics

How to pronounce set theory?

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How to say set theory in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of set theory in Chaldean Numerology is: 9

2. Pythagorean Numerology

   The numerical value of set theory in Pythagorean Numerology is: 9

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=set theory
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Set_Theory
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Set_Theory
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=set theory