In the previous post I discussed the foundations of the differential calculus. Initially defined in the 17

^{th}century in terms of the rather vaguely defined infinitesimals, it was not until the 19^{th}century that Cauchy gave it a rigorous definition with his formalisation of the concept of a limit. Fortunately for us, the infinitesimals were given a solid footing in the 20^{th}century with Conway’s surreal numbers and Robinson’s non-standard numbers, saving us from the annoyingly complex reasoning that Cauchy’s approach requires.Full text...