Set notation - problem

Question

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?

score 3 · Accepted Answer · answered Feb 03 '13 at 18:14

3

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

answered Feb 03 '13 at 18:14

Asaf Karagila

It can be proved that $\mathbb R\cong ~^{\mathbb N}{0,1}$. So $2^{ N}$ is $\mathbb R$ as well. – Mikasa Feb 03 '13 at 18:22
@Babak: Note that in here $N$ is finite, not $\Bbb N$. – Asaf Karagila Feb 03 '13 at 18:32

score 1 · Answer 2 · answered Feb 03 '13 at 18:12

1

Usually it means the power set of $N$.

answered Feb 03 '13 at 18:12

Clayton

score 1 · Answer 3 · answered Feb 03 '13 at 18:35

1

The set of subsets of N .

answered Feb 03 '13 at 18:35

Abhra Abir Kundu

3 Answers3