1

I know how to show that these two have the same cardinality and from that there must be a bijection between them.

Can anyone help with an explicit bijection between these sets?

Asaf Karagila
  • 393,674
MangoPirate
  • 325
  • 1
    $\mathcal P \left({\mathbb{N}}\right)$ and $2^\mathbb{N}$ both denote the power set of $\mathbb{N}$ so I'm not sure what you're asking. – user61031 Feb 06 '13 at 07:29
  • Usually $2^X$ denotes the set of functions $X \to 2$, which is naturally isomorphic to $\mathcal{P}(X)$ (in classical logic anyway...) but is not the same thing. – Trevor Wilson Feb 06 '13 at 07:50

2 Answers2

3

Hint: Think about, given $E\subseteq\mathbb{N}$, the indicator function $\chi_E:\mathbb{N}\to 2$ given by $\chi_E(n)=1$ if $n\in E$ and $0$ otherwise.

Alex Youcis
  • 54,059
2

HINT: Consider indicator (or characteristic) functions of subsets of $\Bbb N$.

Brian M. Scott
  • 616,228