Constructs the quaternions from complex numbers, octonions from quaternions, and keeps doubling like this indefinitely.

Kind of extends the complex numbers.

Some facts that make them stand out:

- one of the only three real associative division algebras in addition to the real numbers and complex numbers, according to the classification of associative real division algebras
- the simplest non-commutative division algebra. Contrast for example with complex numbers where multiplication is commutative

Unlike the quaternions, it is non-associative.