Zero Element of Multiplication on Numbers

Theorem
On all the number systems: the zero element of multiplication is zero ($0$).
 * natural numbers $\N$
 * integers $\Z$
 * rational numbers $\Q$
 * real numbers $\R$
 * complex numbers $\C$

Proof
This is demonstrated by showing that:
 * $n \times 0 = 0 = 0 \times n$

for all $n$ in all standard number systems.

Also see

 * Identity Element of Addition on Numbers
 * Identity Element of Multiplication on Numbers