Exponential Function is Continuous
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Theorem
Real Numbers
The real exponential function is continuous.
That is:
- $\forall x_0 \in \R: \ds \lim_{x \mathop \to x_0} \exp x = \exp x_0$
Complex Numbers
- $\forall z_0 \in \C: \ds \lim_{z \mathop \to z_0} \exp z = \exp z_0$