Definition:Exponential Function/Real

Definition
For all definitions of the real exponential function:


 * The domain of $\exp$ is $\R$


 * The codomain of $\exp$ is $\R_{>0}$

For $x \in \R$, the real number $\exp x$ is called the exponential of $x$.

Notation
The exponential of $x$, $\exp x$, is frequently written as $e^x$. The consistency of this power notation is demonstrated in Equivalence of Definitions of Real Exponential Function.

Also see

 * Equivalence of Definitions of Real Exponential Function
 * Properties of Exponential Function