User:Keith.U/Sandbox/Proof 3

Theorem
Let $e$ denote Euler's Number.

Then $e \in \R$.

Proof
This proof assumes the Base of Logarithm definition of $e$.

That is, let $e$ be the number such that:
 * $\ln e = 1$

where $\ln$ denotes the natural logarithm

From Natural Logarithmn is Bijective, there exists a unique number $e$ such that:
 * $\ln e = 1$

Hence the result.