HallsofIvy said:
Set theory is a branch of mathematics that deals with the study of sets, which are collections of objects or elements. It provides a foundation for all of mathematics and is used to solve problems in various fields such as computer science, statistics, and physics.
The basic operations in set theory are union, intersection, and complement. Union is the combination of two sets, intersection is the common elements between two sets, and complement is the set of all elements that are not in a particular set.
Sets in set theory can be represented in different ways, such as using braces { } and listing the elements, using a roster notation to list the elements, or using set-builder notation to describe the properties of the elements in the set.
The cardinality of a set is the number of elements in a set. It is denoted by |S|, where S is the set. For example, if a set S = {1, 2, 3}, then its cardinality is 3.
A finite set is a set that has a limited number of elements, while an infinite set has an unlimited number of elements. Finite sets can be counted, while infinite sets cannot be fully counted.