Greetings Mike_bb,
I just saw the reply you made at https://math.stackexchange.com/questions/5066589/can-the-order-of-an-infinitesimal-be-non-integer/5069096#5069096
I don't understand the proof you wrote there.
If you can prove
(1) ##c^2\Delta t^2-\Delta x^2 = K(c^2\Delta t'^2-\Delta x'^2)##...