Notes for rough derivatives and rough continuity in rough function model

In the scheme of Pawlak rough derivatives theory, functional features of roughly derived functions and higher order roughly derived functions are directed in rough function model. The valuing laws of first order and higher order roughly derived functions are given in form of a rough derivatives table. According to the difference principle of numerical analysis theory, the higher order rough derivative formula is verified by the notions of unit mapping and identity mapping. On rough continuity of discrete functions in rough function model, the relationship among the ε-δ definition of the rough continuity and two other concepts of Pawlak rough continuity is analyzed. It is proved that these different definitions of the rough continuity are equivalent. The investigation in this article complements and develops the theory of rough derivatives and rough continuity in rough function model, which may provide dependable theoretical foundations for further properties discussions and practical applications of rough function model.