What does $\{0,1\}*\mathbb{N}$ mean? The question is to define a bijection 
$$ f: \{0,1\}*\mathbb{N} \rightarrow \mathbb{N} $$
I can't interpret what does $\{0,1\}*\mathbb{N}$ mean?
Q. Two sets $P$ and $Q$ are given. Question is to define bijection from $P \rightarrow Q$


So, the symbol was just a printing mistake it is the direct product symbol. Now the function can be defined as
$$ f(x,y) = \begin{cases} 2y &\mbox{if } x = 0 \\ 
2y - 1 & \mbox{if } x = 1 \end{cases} $$
Can easily be seen that it is bijective.
