Set theory (nonfiction)

Four iterations of the Cantor set. See Georg Cantor (nonfiction).

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

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  John Venn gathers his thoughts, groups them into logical categories.

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  Writer/sorceror Roger Zelazny (working with artist William Blake) conjures a Venn diagram against an unnamed demon.

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  Venn diagram feeling very colorful today, may play some Fantasy Voronoi diagram.

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  Georg Cantor suffers for his genius, deserves better.

Fiction cross-reference

• John Venn
• Mathematician
• Mathematics

Nonfiction cross-reference

• Georg Cantor (nonfiction)
• Mathematician (nonfiction)
• Mathematics (nonfiction)

External links:

• Set theory @ Wikipedia