# Exponential is Strictly Increasing/Proof 1

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## Theorem

- The function $\map f x = \exp x$ is strictly increasing.

## Proof

By definition, the exponential function is the inverse of the natural logarithm function.

From Logarithm is Strictly Increasing, $\ln x$ is strictly increasing.

The result follows from Inverse of Strictly Monotone Function.

$\blacksquare$