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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 (A_{j})_{j∈J}.## Examples

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## See also

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

- An enumeration of a set S gives an index set $J\; sub\; mathbb\{N\}$, where $f:J\; rarr\; mathbb\{N\}$ 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 $mathbf\{1\}\_rcolon\; mathbb\{R\}\; rarr\; mathbb\{R\}$ given by

- $mathbf\{1\}\_r\; (x)\; :=\; begin\{cases\}\; 0,\; \&\; mbox\{if\; \}\; x\; ne\; r\; 1,\; \&\; mbox\{if\; \}\; x\; =\; r.\; end\{cases\}$

The set of all the $mathbf\{1\}\_r$ functions is an uncountable set indexed by $mathbb\{R\}$.

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Last updated on Saturday September 20, 2008 at 02:56:30 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Saturday September 20, 2008 at 02:56:30 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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