I can generate the sum of all integers and x. I meant to show that $\displaystyle f_n$ has an inverse, $\displaystyle f^{-1} = f_{-n}$

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- Oct 20th 2012, 04:38 PMpirateboyRe: Cyclic group of permutations. f_n(x) = x + n
I can generate the sum of all integers and x. I meant to show that $\displaystyle f_n$ has an inverse, $\displaystyle f^{-1} = f_{-n}$

- Oct 20th 2012, 04:42 PMILikeSerenaRe: Cyclic group of permutations. f_n(x) = x + n
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 f_{3}, f_{6}, f_{9}, ...

Not sure if I get all elements then...? - Oct 20th 2012, 05:16 PMpirateboyRe: Cyclic group of permutations. f_n(x) = x + 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. - Oct 20th 2012, 05:22 PMILikeSerenaRe: Cyclic group of permutations. f_n(x) = x + 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?