\begin{definition}[Definition:Octonion/Addition]
Let $x = \tuple {a, b}$ and $y = \tuple {c, d}$ be octonions, where $a, b, c, d \in \H$ are quaternions.
The '''sum''' of $x$ and $y$ is defined as:
:$x + y = \tuple {a, b} + \tuple {c, d} = \tuple {a + c, b + d}$
Category:Definitions/Octonions
\end{definition}