\begin{definition}[Definition:Lipschitz Quaternion]
A '''Lipschitz quaternion''' is a quaternion whose components are all integers.
The set $\Bbb L$ of all '''Lipschitz quaternions''' can therefore be defined as:
:$\Bbb L = \set {a + b \mathbf i + c \mathbf j + d \mathbf k \in \H: a, b, c, d \in \Z}$
{{NamedforDef|Rudolf Lipschitz|cat=Lipschitz}}
\end{definition}