Exponential Function is Continuous

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Theorem

Real Numbers

The real exponential function is continuous.

That is:

$\forall x_0 \in \R: \displaystyle \lim_{x \mathop \to x_0} \ \exp x = \exp x_0$


Complex Numbers

$\forall z_0 \in \C: \displaystyle \lim_{z \mathop \to z_0} \exp z = \exp z_0$