▾ 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
▾ Ringoid
▾ Semiring
▾ Ring
▾ Additive group
▾ Odd map
Odd euclidean real function
Formulation 0
A D4363: Euclidean real function $f : \mathbb{R}^N \to \mathbb{R}^M$ is odd if and only if \begin{equation} \forall \, x \in \mathbb{R}^N : f(-x) = - f(x) \end{equation}
Child definitions
» D4695: Conjugate-odd complex function
Results
» R2960: Function odd part is odd
» R2929: Sum of odd functions is odd