# Abstract Function

1. Aug 15, 2009

### Zhujiao

1. The problem statement, all variables and given/known data
Function f(x) defined in [0,1],and f(0)=f(1).If $$x_{1},x_{2}\in[0,1]$$ then $$|f(x_{1})-f(x_{2})|<|x_{1}-x_{2}|$$ (*)
Prove $$|f(x_{1}）-f(x_{2}）|<1/2$$

2. Relevant equations
I think maybe |a|-|b|$$\leq$$|a-b|$$\leq$$|a|+|b| will be helpful

3. The attempt at a solution
Well,I get some information from (*),I can prove that f(x)+x is monotone increasing and f（x)-x is monotone decreasing.Then I don't know what I should do. And I'm not sure whether I'm in the right way.

PS: why I can't see LaTex images clearly.They appear to be a black background and letters numbers or signs are not easy to recognize

Last edited: Aug 15, 2009