Let $A=\{ 2+\frac{1}{n+1} ,\quad -2+\frac{1}{n+1} \mid\quad n=0,1,\ldots \}$.
Find a bijection from $\mathbb{Z}$ to $A$.
I try to set $f : \mathbb{Z} \to A $ where $f(k)=2+\frac{1}{k+1}$ if $k\geq 0$ and $f(k)=-2+\frac{1}{k+1} $ if $k <0 $. But this does not work.
Can you give some ideas?
Thank you!