# Bijection of infinite sets

For any set $A$ such that $A$ has a bijection with $A\times A$ , prove that there's a bijection between $P(A)$ and $P(A) \times P(A)$, where $P(A)$ is the power set of $A$.

• There will be a bijection between $P(A)$ and $P(A \times A)$ Does it help ? – user90041 Nov 10 '13 at 19:26

Recall that if $A$ and $B$ are disjoint then $\mathcal P(A)\times\mathcal P(B)$ has a bijection with $\mathcal P(A\cup B)$. Show that the condition of $A$ implies that $A$ and $A\times\{0,1\}$ have a bijection.