That's not correct. Mathematically as they describe the same thing they have to be translatable into each other. But one is a natural mathematical definition, the other exploits a completely unintuitive incidental mathematical isomorphism.
If you would read a few sentences on from where you quote, this becomes evident.
ij = k
is arbitrary, needs to be memorized and just happens to do what you want for reasons that require a lot of working out.
If you would read a few sentences on from where you quote, this becomes evident.
is arbitrary, needs to be memorized and just happens to do what you want for reasons that require a lot of working out. On the other hand requires zero memorization.