Math students know a lot of hard truths about functions: continuity isn't differentiability, integrability isn't continuity, not every function has a Taylor or Fourier series, and when they do these series may not converge to themselves! There are functions that are continuous only on measure-zero sets, there's the Devil's Staircase, there are many terrible things.
In physics classes, some "niceness" is taken for granted: often Taylor approximations are assumed valid, continuity or differentiability is assumed, etc. I could have asked the question, "Is every function in use in Physics differentiable?" But I chose to ask something similar, hopefully more informative. What's the the "worst" function in use in Physics right now?
