(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose f is continuous on [0,2]and thatn f(0) = f(2). Prove that there exists x,y in [0,2] such that |y-x| = 1 and f(x) = f(y)

2. Relevant equations

3. The attempt at a solution

I got the following 1 line proof.

Suppose g(x) = f(x + 2) - f(x) on I = [0,2]

this proofs that |x - y| = 1 for x = 1, y = 2

and f(x) = f(y)

thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Real Analysis: Properties of Continuity

**Physics Forums | Science Articles, Homework Help, Discussion**