# Definition:Lipschitz Quaternion

## Definition

A Lipschitz quaternion is a quaternion whose components are all integers.

The set $\Bbb L$ of all Lipschitz quaternions can therefore be defined as:

$\Bbb L = \left\{{a + b \mathbf i + c \mathbf j + d \mathbf k \in \Bbb H: a, b, c, d \in \Z}\right\}$

## Source of Name

This entry was named for Rudolf Lipschitz.