In article <email@example.com>, Timothy Murphy <firstname.lastname@example.org> wrote:
> Bart Goddard wrote: > > >>> > 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. > >> > >> This sounds ambiguous to me. Do you mean that you don't think it's > >> true that the upper limit is 1 or do you mean that you don't think > >> it's true that it's clear that the upper limit is 1? > > > > Neither. Obviously the thing I don't think is true is the > > sentence to which I'm responding: > > > That the values > > of |sin n|^(1/n) are evenly distributed. You could > > infer this by my coment about the (1/n) power pushing > > things toward zero. > > You seem to be responding to yourself. > I did not say that "|sin n|^(1/n) is evenly distributed". > > > It has already been proven that the limit is 1. > > I think I missed this proof. > What was the essential idea?
Note that for any fixed value, x, between 0 and 1, lim x ^(1/n) = 1 --