Let $x, y \in [0, \infty)$ each be an D4767: Unsigned real number.
Let $p, q \in (0, \infty)$ each be a D5407: Positive real number such that
Let $p, q \in (0, \infty)$ each be a D5407: Positive real number such that
| (i) | \begin{equation} \frac{1}{p} + \frac{1}{q} = 1 \end{equation} |
Then
| (1) | \begin{equation} x y \leq \frac{x^p}{p} + \frac{y^q}{q} \end{equation} |
| (2) | \begin{equation} x y = \frac{x^p}{p} + \frac{y^q}{q} \quad \iff \quad \frac{x^p}{p} = \frac{y^q}{q} \end{equation} |