Thread: Cyclic group of permutations. f_n(x) = x + n

I can generate the sum of all integers and x. I meant to show that has an inverse,

Hmm, if I compose f_n and f_n, I get f_2n.

You did not really say what n is yet.
Suppose I pick n=3.
Then I have f₃, f₆, f₉, ...
Not sure if I get all elements then...?

Errr. Rather The group is, please correct my notation here. is

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.

That would be correct.
The notation would be <f_n> which would have the generator f_n.

However, the problem statement does not mention that cyclic group, does it?

Perhaps you can pick a specific n?