Originally Posted by

**Amanda1990** Here's the question:

"Let K be a compact subset in $\displaystyle \Re$ and let $\displaystyle f : K \rightarrow \Re$ be a continuous function. Prove that for every $\displaystyle \epsilon > 0$ there exists $\displaystyle L_{\epsilon}$ such that

$\displaystyle |f(x) - f(y)| \leq L_{\epsilon} |x-y| + \epsilon$ for every $\displaystyle x,y \in K$."

I don't really see the "point" of the question - can't we just take $\displaystyle L_{\epsilon} = |f(x) - f(y)| / |x-y| $? What are we "supposed" to do?