Exponential of Real Number is Strictly Positive/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 over Rationals.

$\blacksquare$