# Index set

Revision as of 19:32, 26 March 2012 by en>Lifeonahilltop (→Examples)

In mathematics, the elements of a set *A* may be *indexed* or *labeled* by means of a set *J* that is on that account called 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 (*A*_{j})_{j∈J}.

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; i.e., on input 1^{n}, *I* can efficiently select a poly(n)-bit long element from the set.
^{[1]}

## 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 indexed by .

- For , the indicator function on
*r*is the function given by

The set of all the functions is an uncountable set indexed by .

## References

- ↑ {{#invoke:citation/CS1|citation |CitationClass=book }}

## See also

de:Familie (Mathematik) it:Famiglia (matematica) hu:Halmazrendszer nl:Indexverzameling ja:添字記法 no:Familie (matematikk) zh:索引集