October 23, 2017
Differentiability has a very strange and counterintuitive definition, until you think about it with linear approximations in mind. Even better (and not covered in this comic), this definition of differentiability allows us to keep the beloved “differentiability implies continuity” result from single-variable calculus.
This definition of differentiability is known as Fréchet differentiability and is easily extended to vector spaces that are more generic than \( \mathbb{R}^n \) such as Banach spaces and Hilbert spaces.