User:Keith.U/Sandbox/Proof 3

Theorem
Let $x$ be a real number.

Let $\exp$ denote the (real) Exponential Function.

Then:
 * $\forall x \in \R : \exp x > 0$

Proof
This proof assumes the definition of $\exp x$ as the unique continuous extension of $e^x$.

Since $e > 0$, the result follows immediately from Power of Positive Real Number is Positive.