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History. Outline. Index. Mathematics Portal. v. t. e. A Venn diagram illustrating the intersection of two sets. Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.
- Set (Mathematics)
Sets are ubiquitous in modern mathematics. Indeed, set...
- Glossary of Set Theory
1. Naive set theory can mean set theory developed...
- Set (Mathematics)
Beginning. History. Theory. Related pages. References. Further reading. Set theory. A Venn diagram illustrating the intersection of two sets. Set theory is the study of sets in mathematics. Sets are collections of objects. We refer to these objects as "elements" or "members" of the set.
8 de out. de 2014 · First published Wed Oct 8, 2014; substantive revision Tue Jan 31, 2023. Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set. Pure set theory deals exclusively with sets, so the only sets under consideration are those whose members are also sets.
Set theory is a branch of mathematics that studies sets, which are essentially collections of objects. For example \(\{1,2,3\}\) is a set, and so is \(\{\heartsuit, \spadesuit\}\). Set theory is important mainly because it serves as a foundation for the rest of mathematics--it provides the axioms from which the rest of mathematics is built up.
Back to Top. Supplement to Set Theory. Basic Set Theory. Sets are well-determined collections that are completely characterized by their elements. Thus, two sets are equal if and only if they have exactly the same elements. The basic relation in set theory is that of elementhood, or membership.
