ThmDex – An index of mathematical definitions, results, and conjectures.
Subadditivity of basic real square root function
Formulation 0
Let $x_1, \dots, x_N \in [0, \infty)$ each be an D4767: Unsigned real number.
Then \begin{equation} \left( \sum_{n = 1}^N x_n \right)^{1/2} \leq \sum_{n = 1}^N x_n^{1/2} \end{equation}
Formulation 1
Let $x_1, \dots, x_N \in [0, \infty)$ each be an D4767: Unsigned real number.
Then \begin{equation} \sqrt{ \sum_{n = 1}^N x_n } \leq \sum_{n = 1}^N \sqrt{x_n} \end{equation}