| > Because a divisor cannot exist unless it is a multiplicative inverse. Therefore 0 is not a divisor. So there are two separate issues here. One is whether we can extend the definition of the "/" operator, and the other is whether we call it "division". I'm not interested in what we call it. I'm interested in the claim that extending "/" will break the field. The dichotomy you're talking about is wrong. The two options are not "multiplicative inverse" and "does not interact with anything". "1/0 = 0" interacts with plenty! If I make a system where it's an axiom, I can calculate things like "1/0 + 5" or "sqrt(1/0)" or "7/0 + x = 7". I can't use it to cancel out a 0, but I can do a lot with it. > It boggles my mind that there are people in this thread still fighting an idea in earnest which has been settled for over a century. Remember, the question is not "should this be an axiom in 'normal' math?", the question is "does this actually conflict with the axioms of a field?" > You can't just add another axiom to a field and call it a field. Yes you can. There is an entire hierarchy of algebraic structures. Adding non-conflicting axioms to an X does not make it stop being an X. |