Discrete data is categorical data, rather than continuous measurements. It can be treated as continuous data, but that depends on the measurements set. It allows you to quantify things like pass/fail ...

Can discretely sampled financial data help us decide which continuous-time models are sensible? Diffusion processes are characterized by the continuity of their sample paths. This cannot be verified ...

Split a mile in half, you get half a mile. Split the half mile, you get a quarter, and on and on, until you’ve carved out a length far smaller than the diameter of an atom. Can this slicing continue ...