User:Keith.U/Sandbox/Proof 4

Theorem
Let $e$ denote Euler's Number.

Then $e \in \R$.

Proof
This proof assumes the Exponential Function at $1$ definition of $e$.

That is, let:
 * $\exp 1 = e$

where $\exp$ denotes the (real) exponential function.

From Exponential Function is Well-Defined: Real, $\exp$ maps $1$ to a  unique  real number.

Hence the result.