Calculus in a discrete universe Suppose we ascertained that space and time are discrete and the units are Planck's. Would that affect calculus? I know that integration does not require a continuum, but about differentiation I read contrasting views, w.r.t. physical functions. In order to be differentiable a function must be continuous, does that imply that _dx_ must be a _continuum_? Can someone say a final word?

"Would that affect calculus?" Of course not, and calculus in its present form would even remain a perfect tool for describing the macroscopic world. Note that, e.g,. we already _know_ that matter comes in the form of "little balls", but nevertheless we treat it as a homogeneous "glue" when we do elasticity or hydrodynamics.

On the other hand it might be the case that some sort of new mathematics would be needed to describe and understand better time and space in its ultimate fine grained structure.