Index set

In mathematics, an index set is a set whose members label (or index) members of another set.^[1]^[2] For instance, if the elements of a set A may be indexed or labeled by means 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 (A_j)_j∈J.

{{{{{{{Let I be the set of natural numbers then the family of set then the family of set {AI:i€I} is called index family of set and the set a is called an index set

           A.           A
       (1              ( 1
         2.             2
         3).          3)
                            Therefore f:A------> A be a one-time function. }}}}}}}}
   
       DHARMENDRA RAJA

Other uses

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 $1^{n}$ , $I$ can efficiently select a poly(n)-bit long element from the set.^[3]

References

^ Weisstein, Eric. "Index Set". Wolfram MathWorld. Wolfram Research. Retrieved 30 December 2013.
^ Munkres, James R. Topology. Vol. 2. Upper Saddle River: Prentice Hall, 2000.
^ Goldreich, Oded (2001). Foundations of Cryptography: Volume 1, Basic Tools. Cambridge University Press. ISBN 0-521-79172-3.

[1] Weisstein, Eric. "Index Set". Wolfram MathWorld. Wolfram Research. Retrieved 30 December 2013.

[2] Munkres, James R. Topology. Vol. 2. Upper Saddle River: Prentice Hall, 2000.

[3] Goldreich, Oded (2001). Foundations of Cryptography: Volume 1, Basic Tools. Cambridge University Press. ISBN 0-521-79172-3.

[1]

[2]

[3]

Other uses

See also

References