Identity Element of Addition on Numbers

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

This zero is also the zero element of multiplication.

Proof
This is demonstrated in these pages:


 * Natural Number Addition Identity is Zero
 * Integer Addition Identity is Zero
 * Rational Addition Identity is Zero
 * Real Addition Identity is Zero
 * Complex Addition Identity is Zero