High Quality Content by WIKIPEDIA articles! In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold . There are only four such algebras, the other three being the real numbers R, the complex numbers C, and the quaternions 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.