IJ=JK=KI=IJK=I^2=J^2=K^2=-1

IJ=JK=KI=IJK=I^2=J^2=K^2=-1

What could I, J and K be? If you don't answer it means all of maths since the 1840s is a fallacy and anyone who goes past arithmetic and calculus has been fooled.

>>11
Any group {1, -1, i, -i, j, -j, k, -k} whose group operation table is what we expect for the quaternions is isomorphic to the group {U, -U, I, -I, J, -J, K, -K} with U,I,J,K being complex 2x2 matrices. Objecting to my 'defining' the quaternions in terms of those complex matrices is similar to objecting to one of the various constructions of the real numbers by saying that the reals are an arbitrary complete ordered archimedean field. You've added nothing to the conversation but a half-hearted attempt to show off how totally awesome at math you are.