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I have problem with a notation used in an information theory course.

Let $N = \lbrace 1,\dots, n \rbrace$ for $n\in\mathbb{N}$.

What does $2^{N}$ mean/denote?

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3 Answers 3

up vote 3 down vote accepted

It denotes all the binary sequences of length $n$. This set can also be identified with the power set of $N$.

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It can be proved that $\mathbb R\cong ~^{\mathbb N}\{0,1\}$. So $2^{ N}$ is $\mathbb R$ as well. –  Babak S. Feb 3 '13 at 18:22
    
@Babak: Note that in here $N$ is finite, not $\Bbb N$. –  Asaf Karagila Feb 3 '13 at 18:32

Usually it means the power set of $N$.

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The set of subsets of N .

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