ab=ba is not an axiom for integers (where multiplication is defined as repeated addition), or rationals (where multiplication is defined in terms of integer mul

ab=ba is not an axiom for integers (where multiplication is defined as repeated addition), or rationals (where multiplication is defined in terms of integer multiplication). I suspect that it is similarly not an axiom in the real numbers (and, by extension, the complex numbers), but it has been a while since I looked of how the reals were defined. If we consider fields, then the field operation commonanly referred to as multiplication, is defined to be commutative.