Abstract: The distance of fuzzy numbers is used to define both the fuzzy continuous Auctions and the sequent convergence of fuzzy functions. Their properties are also investigated. The results show that both the sum/difference of fuzzy continuous functions are fuzzy continuous functions and if each term is fuzzy continuous functions in sequence of fuzzy functions, its limit is also fuzzy continuous. In case of consistent continuous functions, integral sign and limit sign are interchangeable, so are differential sign and limit sign.