From https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_constru... - "The Hurwitz's theorem

From https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_constru... - "The Hurwitz's theorem (composition algebras) states that the reals, complex numbers, quaternions, and octonions are the only (normed) division algebras (over the real numbers)." So what? From https://en.wikipedia.org/wiki/Sedenion https://en.wikipedia.org/wiki/Sedenion - "Every sedenion is a linear combination of the unit sedenions e_0...e_15 , which form a basis of the vector space of sedenions." - clearly we still have operations to work with. Stopping at octonions looks somewhat arbitrary.