# Law of Division

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## 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

## Sources

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