First 4 (reals, complex, quaternions, octonions) are normed division algebras. Normed means that each number has associated nonnegative real number that descri

First 4 (reals, complex, quaternions, octonions) are normed division algebras. Normed means that each number has associated nonnegative real number that describes the "size" of the number, also |xy| <= |x||y|. Number having a size (a norm) is very useful concept. Sedions and the rest are less useful because they are not normed algebras.