set theory

Table of Contents

Introduction
Introduction to naive set theory
- Fundamental set concepts
  - Operations on sets
  - Relations in set theory
- Essential features of Cantorian set theory
  - Equivalent sets
  - Cardinality and transfinite numbers
Axiomatic set theory
- The Zermelo-Fraenkel axioms
  - Schemas for generating well-formed formulas
  - Axioms for compounding sets
  - Axioms for infinite and ordered sets
  - Schema for transfinite induction and ordinal arithmetic
  - Axiom for eliminating infinite descending species
- The Neumann-Bernays-Gödel axioms
- Limitations of axiomatic set theory
- Present status of axiomatic set theory

References & Edit History Related Topics

Images

$A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”$

For Students

set theory summary

Discover

Space race (1957-1969) infographic between United States (U.S.) and Russia. America, Soviet Union, U.S.S.R., space exploration

Timeline of the Space Race, 1957–69

Bar graph of the United States Death Toll during major events. Infogram chart.

U.S. Death Toll During Major Events

Common, or southern, cassowary (Casuarius casuarius).

8 Birds That Can’t Fly

Ruminant. Deer. Red deer. Cervus elaphus. Buck. Stag. Antlers.

9 of the World’s Deadliest Mammals

22 Questions About Time and Timekeeping Answered

Amendments 1-10 to the Constitution of the United States constitute what is known as the Bill of Rights on an American flag.

What Is the Emoluments Clause?

Why Doesn’t Arizona Observe Daylight Saving Time?

set theory: Related Content

Written and fact-checked by The Information Architects of Encyclopaedia Britannica

Photos

See All Images →

Topics

Venn diagram axiom of choice Zorn’s lemma continuum hypothesis Cantor’s theorem partition axiom of pairing axiom schema of replacement principle of abstraction axiom of infinity analysis probability theory cryptology computer science combinatorics algebra statistics geometry automata theory information theory

Dig Deeper: More Articles That Discuss This Topic

Key People

Georg Cantor

German mathematician

Paul Erdős

Hungarian mathematician

John von Neumann

American mathematician

Saul Kripke

American logician and philosopher

Stanislaw Ulam

American scientist

Paul Joseph Cohen

American mathematician

Quiz

Numbers and Mathematics

set theory: Related Content

Photos

Related Topics and References

Key People

Related Quizzes and Features