, the elements of a set A
may be indexed
by means of a set J
that is on that account called an index set
. The indexing consists of a surjective function
and the indexed collection is typically called an (indexed) family
, often written as (Aj
In 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 1n, I can efficiently select a poly(n)-bit long element from the set.
- An enumeration of a set S gives an index set , where 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 .