Title

Points at Which Continuous Functions Have the Same Height

Article Type

Research Article

Publication Title

Resonance

Abstract

As an easy application of the intermediate value theorem, one can show that for any continuous function f: [0, 1] → ℝ with f (0) = f (1), there are points a, a + 1/2 both in [0, 1] such that f (a) = f (a + 1/2). In this note, we show that this property holds with 1/2 replaced by any number of the form 1/n for a positive integer n. More interestingly, we show that this is false for every number not of the form 1/n.

First Page

591

Last Page

596

DOI

10.1007/s12045-018-0651-x

Publication Date

5-1-2018

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