Exponential Function is Continuous/Real Numbers/Proof 3

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Theorem

The real exponential function is continuous.

That is:

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


Proof

This proof depends on the differential equation definition of the exponential function.

The result follows from Differentiable Function is Continuous.

$\blacksquare$