In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set A may be indexed or labeled by means of the elements of a set J, then J is an index set. The indexing consists of a surjective function from J onto A, and the indexed collection is typically called an indexed family, often written as {Aj}j∈J.
Examples
- An enumeration of a set S gives an index set
, where f: J → S is the particular enumeration of S.
- Any countably infinite set can be (injectively) indexed by the set of natural numbers
.
- For
, the indicator function on r is the function
given by
The set of all such indicator functions, 
Other uses
In computational complexity theory and cryptography, an index set is a set for which there exists an algorithm I that can sample the set efficiently; e.g., on input 1n, I can efficiently select a poly(n)-bit long element from the set.
