Set (mathematics)

In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set may be finite or infinite, depending whether the number of its elements is finite or not. There is a unique set with no elements, called the empty set; a set with a single element is a singleton.

Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous foundations for all branches of mathematics since the first half of the 20th century.