Indexed family
Collection of objects, each associated with an element from some index set / From Wikipedia, the free encyclopedia
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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 and image (that is, indexed families and mathematical functions are technically identical, just points of view are different). Often the elements of the set 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 is called the index set of the family, and is the indexed set.
Sequences are one type of families indexed by natural numbers. In general, the index set is not restricted to be countable. For example, one could consider an uncountable family of subsets of the natural numbers indexed by the real numbers.