Law of Division

Theorem

Let $\mathbb F$ denote one of the following number systems:

rational numbers $\Q$

real numbers $\R$

complex numbers $\C$

Let $a, b \in \mathbb F$ such that $a \ne 0$.

Then there exists a unique $x$ such that:

$a x = b$

$x$ 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: $\text{VI}.$