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.

>>5
No, they aren't 2x2 complex matrices. They're just arbitrary group elements. You can literally define a numbering system as {1, i, j, k} (and their inverses), and those are your numbers; they don't have to "be" anything else.

You can however represent the group using 2x2 complex matrices in a variety of ways; this representation is called clifford(2).

gb2/grouptheory/