Odd Function of Zero is Zero

Theorem
Let $f: \R \to \R$ be an odd function.

Then:
 * $f \left({0}\right) = 0$

Proof
By definition of odd function:
 * $f \left({-x}\right) = -f \left({x}\right)$

and so:

The only real number $a$ for which $a = -a$ is $0$.

Hence the result.