Set theory (nonfiction)

Venn diagram (nonfiction) showing the intersection of sets A and B.

Set theory is the branch of mathematical logic (nonfiction) that studies sets (nonfiction), which informally are collections (nonfiction) of mathematical objects (nonfiction).

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 (nonfiction).

History

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

Paradoxes in naive set theory

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.

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 (nonfiction) 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

• John Venn
• Mathematician
• Mathematics

External links

• Set theory @ Wikipedia