Definition:Euler's Number/Limit of Sequence

Definition
The sequence $\left \langle {x_n} \right \rangle$ defined as $x_n = \left({1 + \dfrac 1 n}\right)^n$ converges to a limit as $n$ increases without bound.

That limit is called Euler's Number and is denoted $e$.

Also see

 * Equivalence of Definitions of Euler's Number