Not quite, that's not the problem. We're in the realm of maths here and therefore of pure abstraction, so that's not the point. Adding terms to the Fourier seri

Not quite, that's not the problem. We're in the realm of maths here and therefore of pure abstraction, so that's not the point. Adding terms to the Fourier series of a square wave you have an overshoot that does not converge to zero as the number of terms goes to infinity. This is called the Gibbs phenomenon https://en.wikipedia.org/wiki/Gibbs_phenomenon https://en.wikipedia.org/wiki/Gibbs_phenomenon