Category Archives: Analysis

Monotonically increasing intervals

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

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Dense Circle

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

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