ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
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▼ Binary cartesian set product
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▼ Enclosed binary operation
▼ Groupoid
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▼ Even map
Definition D3997
Even euclidean real function
Formulation 0
A D4363: Euclidean real function $f : \mathbb{R}^N \to \mathbb{R}^M$ is even if and only if \begin{equation} \forall \, x \in \mathbb{R}^N : f(-x) = f(x) \end{equation}
Children
▶ D4696: Conjugate-even complex function
▶ D5480: Even real function
Results
▶ R4287: Finite product of even complex functions is even
▶ R2928: Finite sum of even euclidean real functions is even
▶ R2959: Function even part is even