Ok, I have this:
where n .
Show that is cyclic.
It is clearly cyclic as all it's elements are equal to 1, but how do I prove it.
Actually, given the notation used by the OP, for all . Even if the OP wrote , then since is distinct in . Now, if , then we still would only have being the -th roots of unity in the case that is rational. But the OP is allowing , which is an interval of the extended reals. We must assume that is defined and .