Distributive Laws/Arithmetic

Theorem
On all the number systems: the operation of multiplication is distributive over addition.
 * natural numbers $$\N$$
 * integers $$\Z$$
 * rational numbers $$\Q$$
 * real numbers $$\R$$
 * complex numbers $$\C$$

Proof
This is demonstrated in these pages:


 * Natural Number Multiplication Distributes over Addition
 * Integer Multiplication Distributes over Addition
 * Rational Multiplication Distributes over Addition
 * Real Multiplication Distributes over Addition
 * Complex Multiplication Distributes over Addition