Set theory (nonfiction): Difference between revisions

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'''Set theory''' is the branch of [[mathematical logic (nonfiction)]] that studies [[sets (nonfiction)]], which informally are [[collections (nonfiction)]] of [[Mathematical object (nonfiction)|mathematical objects (nonfiction)]].
[[File:Venn_A_intersect_B.svg|thumb|The [[Venn diagram (nonfiction)|Venn diagrams]] is a well-known expression of set theory.]]'''Set theory''' is the branch of [[Mathematics (nonfiction)|mathematics]] that studies sets, which informally are collections of mathematical objects.
 
== Description ==


Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.
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 object (nonfiction)|mathematical objects (nonfiction)]].
The modern study of set theory was initiated by [[Georg Cantor (nonfiction)|Georg Cantor]] and [[Richard Dedekind (nonfiction)|Richard Dedekind]] in the 1870s.


== History ==
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 (nonfiction)|axiom of choice]], are the best-known.


The modern study of set theory was initiated by [[Georg Cantor (nonfiction)]] and [[Richard Dedekind (nonfiction)]] in the 1870s.
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.


== Paradoxes in naive set theory ==
== In the News ==


After the discovery of [[paradoxes in naive set theory (nonfiction)]], 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.
<gallery>
File:Cantor set 4 iterations.svg.png|link=Cantor set (nonfiction)|[[Cantor set (nonfiction)|Cantor set]] fundamental to detecting and preventing [[crimes against mathematical constants]], according to recent survey of [[Mathematics|mathematicians]].
File:John Venn computing diagram.jpg|link=John Venn|[[John Venn]] gathers his thoughts, groups them into logical categories.
File:William_Blake_-_Sconfitta_-_Frontispiece_to_The_Song_of_Los.jpg|Writer/sorceror [[Roger Zelazny]] (working with artist [[William Blake]]) conjures a [[Venn diagram]] against an unnamed [[Demon (nonfiction)|Demon]].
File:Georg Cantor 1894.png|link=Georg Cantor (nonfiction)|[[Georg Cantor (nonfiction)|Georg Cantor]] suffers for his genius, deserves better, say Set theory.
</gallery>


== Foundational system ==
== Fiction cross-reference ==


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.
* [[John Venn]]
 
* [[Mathematician]]
== Contemporary research ==
* [[Mathematics]]
 
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 (nonfiction)]] to the study of the [[Large cardinal (nonfiction)|consistency of large cardinals (nonfiction)]].


== Nonfiction cross-reference ==
== Nonfiction cross-reference ==


* [[Mathematical logic (nonfiction)]]
* [[Axiom of choice (nonfiction)]]
* [[Georg Cantor (nonfiction)]]
* [[Graph theory (nonfiction)]]
* [[Mathematician (nonfiction)]]
* [[Mathematician (nonfiction)]]
* [[Mathematics (nonfiction)]]
* [[Mathematics (nonfiction)]]
* [[Large cardinal (nonfiction)]]
* [[Naive set theory (nonfiction)]]
* [[Permutation (nonfiction)]]
* [[Set-builder notation (nonfiction)]]
* [[Set (mathematics) (nonfiction)]]
* [[Uncountable set (nonfiction)]]


== Fiction cross-reference ==
External links:


* [[John Venn]]
* [https://en.wikipedia.org/wiki/Set_theory Set theory] @ Wikipedia
* [[Mathematician]]
* [[Mathematics]]


== External links ==
[[Category:Nonfiction (nonfiction)]]
 
[[Category:Mathematics (nonfiction)]]
* [https://en.wikipedia.org/wiki/Set_theory Set theory] @ Wikipedia
[[Category:Set theory (nonfiction)]]

Latest revision as of 09:18, 5 January 2019

The Venn diagrams is a well-known expression of set theory.

Set theory is the branch of mathematics that studies sets, which informally are collections of mathematical 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 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.

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.

In the News

Fiction cross-reference

Nonfiction cross-reference

External links:

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