          # Set (mathematics)

• a set of polygons in an euler diagram

in mathematics, a set is a well-defined collection of distinct objects, considered as an object in its own right. for example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2, 4, 6}. the concept of a set is one of the most fundamental in mathematics. developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived.

• etymology
• definition
• set notation
• membership
• cardinality
• special sets
• basic operations
• applications
• axiomatic set theory
• principle of inclusion and exclusion
• de morgan's laws
## This article is about what mathematicians call "intuitive" or "naive" set theory. For a more detailed account, see Naive set theory. For a rigorous modern axiomatic treatment of sets, see Set theory. A set of polygons in an Euler diagram In mathematics, a set is a well-defined collection of distinct objects, considered as an object in its own right. For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2, 4, 6}. The concept of a set is one of the most fundamental in mathematics. Developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. Contents 1 Etymology 2 Definition 3 Set notation 3.1 Roster notation 3.2 Set-builder notation 3.3 Other ways of defining sets 4 Membership 4.1 Subsets 4.2 Partitions 4.3 Power sets 5 Cardinality 6 Special sets 7 Basic operations 7.1 Unions 7.2 Intersections 7.3 Complements 7.4 Cartesian product 8 Applications 9 Axiomatic set theory 10 Principle of inclusion and exclusion 11 De Morgan's laws 12 See also 13 Notes 14 References 15 External links  