set theory summary

Written and fact-checked by The Editors of Encyclopaedia Britannica

Below is the article summary. For the full article, see set theory.

set theory, Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its terminology and concepts. These include the operations of union (∪), and intersection (∩). The union of two sets is a set containing all the elements of both sets, each listed once. The intersection is the set of all elements common to both original sets. Set theory is useful in analyzing difficult concepts in mathematics and logic. It was placed on a firm theoretical footing by Georg Cantor, who discovered the value of clearly formulated sets in the analysis of problems in symbolic logic and number theory.

Saul Kripke Summary

Saul Kripke American logician and philosopher who from the 1960s was one of the most powerful and influential thinkers in contemporary analytic (Anglophone) philosophy. Kripke began his important work on the semantics of modal logic (the logic of modal notions such as necessity and possibility)

John von Neumann Summary

John von Neumann Hungarian-born American mathematician. As an adult, he appended von to his surname; the hereditary title had been granted his father in 1913. Von Neumann grew from child prodigy to one of the world’s foremost mathematicians by his mid-twenties. Important work in set theory

Paul Erdős Summary

Paul Erdős Hungarian “freelance” mathematician (known for his work in number theory and combinatorics) and legendary eccentric who was arguably the most prolific mathematician of the 20th century, in terms of both the number of problems he solved and the number of problems he convinced others to

Georg Cantor Summary

Georg Cantor was a German mathematician who founded set theory and introduced the mathematically meaningful concept of transfinite numbers, indefinitely large but distinct from one another. Cantor’s parents were Danish. His artistic mother, a Roman Catholic, came from a family of musicians, and his