A Rough Set Describe Method for Real Function Continuous Theorem

In this paper, a rough set describes method for real functions continuous theorem (the monotone convergence theorem, the Bollzano-Weierstrass theorem, and the nested interval theorem) is proposed. The method describes the process of using real number set infimum and supremum is a precise interval, which is, consists of the lower-approximation and the upper-approximation of rough set This method will widely to the interval series convergence related to problems. These conclusions are helpful for people to understand the essence of rough set theory and rough set method. It provides the new mathematical theory and technique in solving real function continuous problem