On Friday, November 8, 2013 6:10:06 PM UTC, Bart Goddard wrote: > Timothy Murphy <email@example.com> wrote in news:l5dg9v$tn6$1@dont- > > email.me: > > > > > It's clear that the upper limit is 1, > > > since n pi mod Z will be distributed evenly in [0,1), > > > and so will infinitely often be in the range (1/3,2/3). > > > > I don't think this is true. |Sin(n)| is probably > > distributed evenly, but raising to (1/n) power is going > > to crowd things toward 0.
I think the argument is that you can find large n such that |sin(n)| is close to 1. Then 1/n is close to 0 so the upper limit in question tends to 1 because N1 ^ N2 tends to 1 if N1 tends to 1 and N2 tends to 0.
So I'd agree with Timothy Murphy about the clarity of the upper limit being 1. I think you may be thinking of |sin(n)| ^ n. This is a case where the proof of whatever the upper limit is would be much deeper than the above.