Exponential of Real Number is Strictly Positive

Theorem
Let $x$ be a real number.

Then:
 * $\exp x = \displaystyle \lim_{n \to \infty} \left({1 + \frac x n}\right)^n > 0$

where $\exp$ is the third definition of exponential.

Proof
When $n$ is larger than the negative of $x$:

Since $n$ is sufficiently large, $n$ is always larger than the negative of $x$, so $1 + \dfrac x n$ is always positive: