Definition:Exponential Function/Real/Limit of Sequence

Definition
Let $\exp: \R \to \R_{>0}$ denote the (real) exponential function. The exponential function can be defined as the following limit of a sequence:
 * $\exp x := \displaystyle \lim_{n \mathop \to +\infty} \paren {1 + \frac x n}^n$

for all $x \in \R$.

The number $\exp x$ is called the exponential of $x$.

Also see

 * Real Sequence $\paren {1 + \dfrac x n}^n$ is Convergent, demonstrating that this definition is valid