# Set notation - problem

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?

-

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

-
It can be proved that $\mathbb R\cong ~^{\mathbb N}\{0,1\}$. So $2^{ N}$ is $\mathbb R$ as well. –  B.S. Feb 3 at 18:22
@Babak: Note that in here $N$ is finite, not $\Bbb N$. –  Asaf Karagila Feb 3 at 18:32
Usually it means the power set of $N$.