Index set

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. 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. The set of all the 1 r {displaystyle mathbf {1} _{r}} functions is an uncountable set indexed by R {displaystyle mathbb {R} } . In computational complexity theory and cryptography, an index set is a set for which there exists an algorithm I {displaystyle I} that can sample the set efficiently; e.g., on input 1 n {displaystyle 1^{n}} , I {displaystyle I} can efficiently select a poly(n)-bit long element from the set.