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:

$x := b - a$

Proof

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Sources

• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1.1$. Number Systems: $\text{III}.$