Let $f : (0, \infty) \to (0, \infty)$ be a D4364: Real function such that
Let $x, y \in (0, \infty)$ each be a D5407: Positive real number.
(i) | $p \in (0, \infty)$ is a D5407: Positive real number |
(ii) | \begin{equation} f(t) = t^p \end{equation} |
Then
\begin{equation}
x < y
\quad \implies \quad
f(x) < f(y)
\end{equation}