Let $p_1, p_2, \, \ldots, \, p_N \in (0, 1]$ each be a D993: Real number such that

(i)	\begin{equation} \sum_{n = 1}^N p_n = 1 \end{equation}

Let $\log_a$ be the D866: Standard real logarithm function in base $a \in (0, \infty) \setminus \{ 1 \}$.

Then

(1)	\begin{equation} - \sum_{n = 1}^N p_n \log_a p_n \leq \log_a N \end{equation}
(2)	\begin{equation} - \sum_{n = 1}^N p_n \log_a p_n = \log_a N \quad \iff \quad p_1 = p_2 = \cdots = p_N = \frac{1}{N} \end{equation}