Since $e$ is a real number I know that $e^0 = 1$, but when I enter $z=0$ into the power series definition of $e^z$ I get an output of $0$. Am I doing something wrong?
$$e^z = \sum_{n=0}^\infty \frac{1}{n!}z^n$$
Setting $z=0$:
$$e^0 = \sum_{n=0}^\infty \frac{1}{n!}0^n = \sum_{n=0}^\infty 0 = 0$$
What have I done wrong?