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Concept
Index set
Summary
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.
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, , is an uncountable set indexed by .
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.
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