# Necessity of infinitesimal steps for reversible processes

Is there a mathematical proof for why a reversible process is one that has many infinitesimal equilibrium steps, rather than fewer large steps?

Maybe something along the lines of this?:

$$\lim_{\Delta\rightarrow0}[f(\Delta,r,....)]=0$$

where $\Delta$ is the step size, $r$ the distance and $f$ the energy loss of the system.