Smoothness

noun

1. The condition of being smooth; the degree or measure of said condition.
2. (of a function) The highest order of derivative (the differentiability class) over a given domain.

   "Smoothness can vary from 0 (for a nondifferentiable function) to infinity (for a smooth function)."

3. (approximation theory, numerical analysis, of a function) The quantity measured by the modulus of smoothness.