User:Keith.U/Sandbox/Proof 2

Theorem
Let $e$ denote Euler's Number.

Then $e \in \R$.

Proof
This proof assumes the sequence definition of $e$.

That is, let:
 * $\displaystyle e = \lim_{n \to \infty} \left({ 1 + \frac{1}{n} }\right)^{n}$

From One Plus Reciprocal to the Nth:
 * $\displaystyle \left({ 1 + \frac{1}{n} }\right)^{n}$ converges

Hence the result.