Exponential is Strictly Increasing/Proof 1
Jump to navigation
Jump to search
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.
$\blacksquare$