User:Keith.U/Whatever/Definition:Exponential/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 $x$.

Equivalence of Definitions
As shown in Equivalence of Definitions of Exponential Function the definitions above are equivalent.

Notation
The exponential of $x$, $\exp x$, is frequently written as $e^x$. The consistency of this power notation is demonstrated in Exp x equals e^x for Rational Numbers.

Also see

 * Properties of Exponential Function