In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter ${\mathbb O}$. There are only four such algebras, the other three being the real numbers $\Bbb R$, the complex numbers $\Bbb C$, and the quaternions $\Bbb H$. The octonions are the largest such algebra, with eight dimensions, double the number of the quaternions from which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity, power associativity.