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 (Aj)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 1n, 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