▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map
▾ Operation
▾ N-operation
▾ Binary operation
▾ Enclosed binary operation
▾ Groupoid
▾ Semigroup
▾ Standard N-operation
▾ Mean
▾ Complex mean
▾ Real mean
Real exponential mean
Formulation 0
Let $x_1, \dots, x_N \in \mathbb{R}$ each be a D993: Real number.
A D993: Real number $a \in \mathbb{R}$ is an exponential mean of $x_1, \dots, x_N$ if and only if \begin{equation} \sum_{n = 1}^N e^a = \sum_{n = 1}^N e^{x_n} \end{equation}