3 ms·

> there are only three objects satisfying this criteria: the real numbers themselves, the complex numbers, and the quaternions. Does a proof exist that these a

by j1vms 8y ago

> there are only three objects satisfying this criteria: the real numbers themselves, the complex numbers, and the quaternions. Does a proof exist that these are the only three of such objects?

joppy 8y ago
Yes, and the proof only uses linear algebra: https://en.wikipedia.org/wiki/Frobenius_theorem_(real_division_algebras) https://en.wikipedia.org/wiki/Frobenius_theorem_(real_divisi...
- j1vms 8y ago
  Thanks. Great result, surprising for 1877.