You might be more interested in the linked page on proper multiplicative calculus then, https://github.com/Ericson2314/baccumulation/blob/main/math/multiplicati

You might be more interested in the linked page on proper multiplicative calculus then, https://github.com/Ericson2314/baccumulation/blob/main/math/multiplicative-calculus.md https://github.com/Ericson2314/baccumulation/blob/main/math/... . That, in turn, is mostly just a retelling of doi:10.1016/j.jmaa.2007.03.081 I submit two claims basically, in response to what you are saying: - The "proper" multiplicative calculus with limits is no more broken than its additive counterpart - These multiplicative infinitesimals are no more broken than their additive counterparts It seems like you were trying to hold these multiplicative infinitesimals to the standard of calculus with limits, and rejecting them on those grounds. To that rejection, I just say that these infinitesimals were never meant to meet that standard. :)