Exponential Function is Continuous/Real Numbers/Proof 5

Proof
This proof depends on the series definition of $\exp$.

That is, let:
 * $\displaystyle \exp x = \sum_{k \mathop = 0}^{\infty} \frac{x^k}{k!}$

From Series of Power over Factorial Converges, the radius of convergence of $\exp$ is $\infty$.

Thus, from Power Series Converges to Continuous Function, $\exp$ is continuous on $\R$.