Set theory (nonfiction): Difference between revisions
No edit summary |
|||
| Line 1: | Line 1: | ||
[[File:Venn_A_intersect_B.svg|thumb|[[Venn diagram (nonfiction)]] showing the intersection of sets A and B.]]'''Set theory''' is the branch of [[Mathematics (nonfiction)|mathematics]] that studies sets, which informally are collections of mathematical objects. | [[File:Venn_A_intersect_B.svg|thumb|[[Venn diagram (nonfiction)]] showing the intersection of sets A and B.]]'''Set theory''' is the branch of [[Mathematics (nonfiction)|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. | 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 language of set theory can be used in the definitions of nearly all mathematical objects. | ||
[[File:Georg Cantor 1894.png|thumb|100px|link=Georg Cantor (nonfiction)|[[Georg Cantor (nonfiction)|Georg Cantor]] (1894).]]The modern study of set theory was initiated by [[Georg Cantor (nonfiction)|Georg Cantor]] and Richard Dedekind in the 1870s. | [[File:Georg Cantor 1894.png|thumb|100px|link=Georg Cantor (nonfiction)|[[Georg Cantor (nonfiction)|Georg Cantor]] (1894).]]The modern study of set theory was initiated by [[Georg Cantor (nonfiction)|Georg Cantor]] and Richard Dedekind in the 1870s. | ||
| Line 17: | Line 13: | ||
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. | 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 == | ||
<gallery mode="traditional"> | |||
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]]. | |||
</gallery> | |||
== Fiction cross-reference == | == Fiction cross-reference == | ||
* [[John Venn]] | * [[John Venn]] | ||
| Line 35: | Line 26: | ||
* [[Mathematics]] | * [[Mathematics]] | ||
== External links | == Nonfiction cross-reference == | ||
* [[Georg Cantor (nonfiction)]] | |||
* [[Mathematician (nonfiction)]] | |||
* [[Mathematics (nonfiction)]] | |||
External links: | |||
* [https://en.wikipedia.org/wiki/Set_theory Set theory] @ Wikipedia | * [https://en.wikipedia.org/wiki/Set_theory Set theory] @ Wikipedia | ||
Revision as of 17:28, 15 June 2016
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 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.
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.
In the News
John Venn gathers his thoughts, groups them into logical categories.
Writer/sorceror Roger Zelazny (working with artist William Blake) conjures a Venn diagram against an unnamed demon.
Fiction cross-reference
Nonfiction cross-reference
External links:
- Set theory @ Wikipedia