Definition:Odd Function

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Let $X \subset \R$ be a symmetric set of real numbers:

$\forall x \in X: -x \in X$

A real function $f: X \to \R$ is an odd function if and only if:

$\forall x \in X: \map f {-x} = -\map f x$


Identity Function

Let $I_\R: \R \to \R$ denote the identity function on $\R$.

Then $I_\R$ is an odd function.

Also see

  • Results about odd functions can be found here.