Concept

Indexed family

Summary
In mathematics, a family, or indexed family, is informally a collection of objects, each associated with an index from some index set. For example, a family of real numbers, indexed by the set of integers, is a collection of real numbers, where a given function selects one real number for each integer (possibly the same) as indexing. More formally, an indexed family is a mathematical function together with its domain I and X (that is, indexed families and mathematical functions are technically identical, just point of views are different). Often the elements of the set X are referred to as making up the family. In this view, indexed families are interpreted as collections of indexed elements instead of functions. The set I is called the index set of the family, and X is the indexed set. Sequences are one type of families indexed by natural numbers. In general, the index set I is not restricted to be count
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