Law of Subtraction

Theorem
On the following number systems:


 * integers $\Z$
 * rational numbers $\Q$
 * real numbers $\R$
 * complex numbers $\C$

there exists a unique $x$ such that:
 * $a + x = b$

for every given $a$ and $b$.

$x$ is then defined and denoted:
 * $x := b - a$