MathDB

Construct a continuous function satisfying conditions

Source:

October 4, 2010

functionalgebracontinuous functionIMO ShortlistIMO Longlist

Problem Statement

(SWE 2)

For each

\lambda (0 < \lambda < 1

and

\lambda = \frac{1}{n}

for all

n = 1, 2, 3, \cdots)

, construct a continuous function

f

such that there do not exist

x, y

with

0 < \lambda < y = x + \lambda \le 1

for which

f(x) = f(y).