I can generate the sum of all integers and x. I meant to show that $\displaystyle f_n$ has an inverse, $\displaystyle f^{-1} = f_{-n}$
Errr. Rather The group is, please correct my notation here. is $\displaystyle \left< x + n\mathbb{Z}\right>$
The generator would be x + n?
That is for all x in reals, for some integer n, I can generate sum of x and all integer multiples of n.