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An indexed family is a collection of objects that are indexed by some indices. They are denoted as \{A_i\}_{i\in I} .

Definition

Let S be a set. Let I be a set.

Then, a family of elements of S indexed by elements of I is a mapping a:I\to S .

I is called the indexing set.

Notation

The image of an element of I is denoted as S_i .

That is, a(i)=S_i .

A a family of elements of S indexed by I is denoted as \{S_i\}_{i\in I} . If the indexing set is known, they may be denoted as \{S_i\} .

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