\begin{definition}[Definition:Exponential Function/Real/Limit of Sequence]
Let $\exp: \R \to \R_{>0}$ denote the '''(real) exponential function'''.
The '''exponential function''' can be defined as the following limit of a sequence:
:$\exp x := \ds \lim_{n \mathop \to +\infty} \paren {1 + \frac x n}^n$
for all $x \in \R$.
The number $\exp x$ is called the '''exponential of $x$'''.
\end{definition}