Let $\mathbb{Z}$ be the
D367: Set of integers such that
| (i) |
$\cdot : \mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}$ is the D608: Integer multiplication operation
|
| (ii) |
\begin{equation}
\mathbb{Z}_{\neq 0}
: = \mathbb{Z} \setminus \{ 0 \}
\end{equation}
|
| (iii) |
\begin{equation}
{\sim}
: = \left\{ ((a, b), (c, d)) \in (\mathbb{Z} \times \mathbb{Z}_{\neq 0})^2 : a \cdot d = b \cdot c \right\}
\end{equation}
|
The
set of rational numbers is the
D180: Quotient set
\begin{equation}
\mathbb{Q}
: = (\mathbb{Z} \times \mathbb{Z}_{\neq 0}) / {\sim}
\end{equation}
