Euler's Number as Limit of 1 + Reciprocal of n to nth Power/Proof 1

Proof
By definition of the real exponential function as the limit of a sequence:


 * $(1): \quad \exp x := \displaystyle \lim_{n \mathop \to \infty} \paren {1 + \frac x n}^n$

By definition of Euler's number:


 * $e = e^1 = \exp 1$

The result follows by setting $x = 1$ in $(1)$.