Hi, I don't understand why mathematicians would need to define the mathematical concepts of diffferentiabilty and conitnuity. To be honest, I don't even understand why "f(x) tends to f(a) as x tends to a" describes continuity. Also, I am wondering why f(x) = mod x is not differentiable at the origin. Surely, f(x) can have two tangents with opposite orientations at the origin, can't it?? Please help!!