Infinitesimals have a long and complicated history (e.g. 1 = 0.999...) and their lack of a formal definition until recent years has lead to erroneous arguments

Infinitesimals have a long and complicated history (e.g. 1 = 0.999...) and their lack of a formal definition until recent years has lead to erroneous arguments such as thinking that (dx/dy) (dy/dz) (dz/dx) equals 1: https://en.wikipedia.org/wiki/Triple_product_rule https://en.wikipedia.org/wiki/Triple_product_rule