\begin{omgroup}[id=sec.differentiable]{Differentiable Functions} \begin{module}[id=differentiable] \importmodule[load=continuous]{continuous} \symdef{difffunctions}[2]{\mathcal{C}^1(#1,#2)} \abbrdef{DiffRR}[2]{\difffunctions\RealNumbers\RealNumbers} \begin{definition} A function $\fun{f}\RealNumbers\RealNumbers$ is called {\defi{differentiable}} at $\inset{x}\RealNumbers$, iff for all $\epsilon>0$ there is a $\delta>0$, such that $\rfrac{\absval{f(x)-f(y)}}{\absval{x-y}}<\epsilon$ for all $\absval{x-y}<\delta$. \end{definition} \end{module} \end{omgroup} %%% Local Variables: %%% mode: LaTeX %%% TeX-master: "paper" %%% End: