An indexed family is a collection of objects that are indexed by some indices. They are denoted as .
Let be a set. Let be a set.
Then, a family of elements of indexed by elements of is a mapping .
is called the indexing set.
The image of an element of is denoted as .
That is, .
A a family of elements of indexed by is denoted as . If the indexing set is known, they may be denoted as .