
Recent Posts
Archives
Categories
Meta
Advertisements
ProblemĀ A real sequence satisfies for all , where . Let be the length of the th interval. Show that there exists a unique such that for all . RemarkĀ This is a problem that arises from nonlinear quantization in … Continue reading
Proposition 1. Let be an irrational number and denote the set of fractional parts of for all . Then is dense in . Proof. We shall first prove that is dense at , then proceed to the whole range of … Continue reading