Suppose that $\displaystyle f : \Re \rightarrow \Re$ is such that, for some $\displaystyle \epsilon > 0$, if $\displaystyle x,y \in \re$, then $\displaystyle |f(x)-f(y)|<|x-y|^{1+\epsilon}$. Prove that $\displaystyle f$ is constant.Problem Statement:

I dont see how this is true. for instance, $\displaystyle f(x)=x/100$. Is there something I am missing?