# 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 $x$.