Mathematics - Set

A set is a collection of distinct objects, considered as an object in its own right.

The mathematical concept of a set is a group of unique items, meaning that the group contains no duplicates.

Sets are one of the most fundamental concepts 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.

In mathematics education, elementary topics such as Venn diagrams are taught at a young age, while more advanced concepts are taught as part of a university degree.

The familiar Venn Diagrams is used:

• in mathematics education to introduce elementary element of set theory such as “set intersection” and “set union”
• illustrate simple set relationships

Sets are fundamental to logic, mathematics, and computer science, but also practical in everyday applications in business and systems.

Some real-world examples of sets include the following:

• The set of uppercase letters 'A' through 'Z'
• The set of nonnegative integers {0, 1, 2 …}
• The set of reserved Java programming language keywords {'import', 'class', 'public', 'protected'…}
• A set of people (friends, employees, clients, …)
• The set of records returned by a database query
• The set of Component objects in a Container
• The set of all pairs
• The empty set {}

• The idea of a "connection pool" is a set of open connections to a database server.
• Web servers have to manage sets of clients and connections.
• File descriptors provide another example of a set in the operating system.

The basic properties of sets:

• Sets contains only one instance of each item
• Sets may be finite or infinite
• Sets can define abstract concepts

• Set
• Venn_diagram
• Introduction to the Collections Framework