\begin{definition}[Definition:Differentiable Mapping/Real Function/Real Number Line]
Let $f$ be a real function defined on $\R$.
By definition, $\R$ is an (unbounded) open interval.
Let $f$ be differentiable on the open interval $\R$.
That is, let $f$ be differentiable at every point of $\R$.
Then $f$ is '''differentiable everywhere (on $\R$)'''.
Category:Definitions/Differentiable Real Functions
\end{definition}