Definition:Euler's Number

As the Base of the Natural Logarithm
As the base of the Natural Logarithm:

In Terms of the Exponential Function
In terms of the Exponential Function:

Also known as
Euler's Number is also known as Napier's Constant for John Napier.

Also see

 * Equivalence of Definitions of Euler's Number


 * Euler's Number is Irrational


 * Do not confuse with Euler's constant, also known as the Euler-Mascheroni constant

Comment
This is the most famous irrational constant in mathematics after $\pi$ (pi), and equally far-reaching in scope and usefulness.