Collections

Collections are accumulations of items treated as a single unit. In mathematics, a collection is any group of objects that can be identified as its members. When membership is defined by a precise, universal criterion and the collection is not inherently larger than a set, the collection is called a set. If the collection is too large to be a set, some foundational theories refer to it as a proper class. In everyday language, collections are often curated groups, such as stamps, books, or coins.

Set theory defines basic operations on collections: membership tests (whether an object is in a collection), unions, intersections, and Cartesian products. The power set contains all possible subsets. Sets are typically considered unordered, with no duplicates; two sets are equal if they have the same elements. Finite sets have a finite cardinality, while infinite sets can be put into one-to-one correspondences with natural numbers or other well-known infinities.

Several variations of collections exist. A multiset allows repeated elements; a sequence or list records an ordered collection of elements. In computer science, a collection usually refers to an abstract data type with operations such as add, remove, contains, and size, and with concrete implementations including lists, sets, maps, and queues. The performance of operations depends on the chosen representation.

Beyond theory and programming, collections are central to libraries, museums, and personal collecting practices. They are subject to cataloging, provenance assessment, and curation, and they support research, education, and cultural preservation.