Set theory is the branch of mathematical logic that studies sets, informally described as collections of objects, along with their sizes, structures and the axioms that can found the rest of mathematics upon them. It emerged in the 1870s through the work of Georg Cantor and Richard Dedekind. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Central QuestionWhat are the possible sizes of infinite collections, and what axioms can consistently and completely found the rest of mathematics on the notion of a set? 1 Key DebateWhether the axiom of choice, which guarantees a selection function for any collection of nonempty sets without constructing one, should be accepted as a foundational axiom. Zermelo-Fraenkel set theory adopts it as standard (ZFC), but constructivist mathematicians reject the non-computable objects it entails, and Bertrand Russell's discovery that unrestricted set formation produces contradictions forced the field away from naive set theory entirely. 1 Set Theory
Connections
Associated With
Founder of set theory, 1870s.
Source Set Theory (Wikipedia)
Includes
Source Cantor Set (Wikipedia)
Sources
1. Set Theory (Wikipedia)
WikipediaLead and origins sections
the branch of mathematical logic that studies sets, which can be informally described as collections of objects
Origins and central questions
Cantor is commonly considered the founder of set theory
Notable debates section
Let R be the set of all sets that are not members of themselves
Associated With: Georg Cantor, Origins section
Cantor is commonly considered the founder of set theory
View the Source Cantor Set (Wikipedia)
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