Limits and calculus isn’t what I think of, at all, when I think of division. I pretty much limit it exclusive to the multiplicative inverse in mathematical systems where addition and multiplication work like you think they ought to. There are axioms that encompass all of “works like you think they ought to”, and a necessary one of them is the multiplicative inverse of zero is not a number.
Limits and calculus isn’t what I think of, at all, when I think of division. I pretty much limit it exclusive to the multiplicative inverse in mathematical systems where addition and multiplication work like you think they ought to. There are axioms that encompass all of “works like you think they ought to”, and a necessary one of them is the multiplicative inverse of zero is not a number.