Set theory (nonfiction): Difference between revisions
No edit summary |
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 | [[File:Venn_A_intersect_B.svg|thumb|[[Venn diagram (nonfiction)]] showing the intersection of sets A and B.]]'''Set theory''' is the branch of mathematical logic that studies sets, which informally are collections of mathematical objects. | ||
== Description == | == Description == | ||
| Line 5: | Line 5: | ||
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 | The language of set theory can be used in the definitions of nearly all mathematical objects. | ||
== History == | == History == | ||
The modern study of set theory was initiated by [[Georg Cantor (nonfiction)]] and | The modern study of set theory was initiated by [[Georg Cantor (nonfiction)]] and Richard Dedekind]] in the 1870s. | ||
== Paradoxes in naive set theory == | == Paradoxes in naive set theory == | ||
After the discovery of | 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. | ||
== Foundational system == | == Foundational system == | ||
| Line 23: | Line 23: | ||
Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community. | 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 | 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 [[Large cardinal (nonfiction)|consistency of large cardinals (nonfiction)]]. | ||
== Nonfiction cross-reference == | == Nonfiction cross-reference == | ||
Revision as of 07:08, 30 May 2016
Set theory is the branch of mathematical logic 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.
The language of set theory can be used in the definitions of nearly all mathematical objects.
History
The modern study of set theory was initiated by Georg Cantor (nonfiction) and Richard Dedekind]] in the 1870s.
Paradoxes in naive set theory
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.
Foundational system
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.
Contemporary research
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 (nonfiction).
Nonfiction cross-reference
- Mathematical logic (nonfiction)
- Mathematician (nonfiction)
- Mathematics (nonfiction)
- Large cardinal (nonfiction)
- Permutation (nonfiction)
- Set (mathematics) (nonfiction)
Fiction cross-reference
External links
- Set theory @ Wikipedia