Sets

Sets are a fundamental concept in mathematics, specifically in the branch known as set theory. They are abstract collections of distinct objects, considered as an object in their own right. Sets are one of the most basic building blocks in mathematics.

Definition

In mathematics, a set is a collection of distinct objects, considered as an object in its own right. For example, the numbers 1, 2, and 3 are distinct objects when considered separately, but when they are considered collectively they form a single set of three elements, denoted {1,2,3}. Sets are one of the most fundamental concepts in mathematics.

History

The concept of a set was developed by Georg Cantor, a German mathematician, in the late 19th century. Cantor's work on set theory became the foundation for much of modern mathematics.

Basic Concepts

Elements

An element is an object that belongs to a set. For example, in the set {1,2,3}, the numbers 1, 2, and 3 are elements of the set.

Subsets

A subset is a set that is contained within another set. For example, the set {1,2} is a subset of the set {1,2,3}.

Union and Intersection

The union of two sets is a set that contains all elements that are in either set. The intersection of two sets is a set that contains all elements that are in both sets.

Applications

Sets are used in nearly every branch of mathematics. They are used in probability theory to define events, in geometry to define shapes, and in algebra to define structures.

See Also

• Set theory
• Georg Cantor
• Mathematics