Odd Function of Zero is Zero

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

Let $f$ be defined at the point $x = 0$.

Then:
 * $\map f 0 = 0$

Proof
By definition of odd function:
 * $\map f {-x} = -\map f x$

and so:

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

Hence the result.