ThmDex – An index of mathematical definitions, results, and conjectures.
▼ 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
Definition D3998
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}
Children
▶ D4695: Conjugate-odd complex function
Results
▶ R2960: Function odd part is odd
▶ R2929: Sum of odd functions is odd