- Index set
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 asurjective function from "J" onto "A" and the indexed collection is typically called an "(indexed) family", often written as ("A"_{"j"})_{"j"∈"J"}.In

complexity theory andcryptography , an index set is a set for which there exists an algorithm "I" that can sample the set efficiently; i.e., on input 1^{n}, "I" can efficiently select a poly(n)-bit long element from the set. [*cite book*]

title= Foundations of Cryptography: Volume 1, Basic Tools

last= Goldreich

first= Oded

year= 2001

publisher= Cambridge University Press

isbn= 0-521-79172-3**Examples***An

enumeration of a set "S" gives an index set $J\; sub\; mathbb\{N\}$, where $f:J\; arr\; mathbb\{N\}$ is the particular enumeration of "S".*Any

countably infinite set can be indexed by $mathbb\{N\}$.*For $r\; in\; mathbb\{R\}$, the

indicator function on r, is the function $mathbf\{1\}\_rcolon\; mathbb\{R\}\; arr\; mathbb\{R\}$ given by:$mathbf\{1\}\_r\; (x)\; :=\; egin\{cases\}\; 0,\; mbox\{if\; \}\; x\; e\; r\; \backslash \; 1,\; mbox\{if\; \}\; x\; =\; r.\; end\{cases\}$

The set of all the $mathbf\{1\}\_r$ functions is an

uncountable set indexed by $mathbb\{R\}$.**References****ee also*** Index

* Indexed family

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