In view of computability for functions on the set , this method cannot be applied for introducing computability on uncountable sets M like the set R of real numbers. The above concepts will be extended to uncountable set by using infinite sequences of symbols of names and by defining computability for functions which transform such infinite sequences with Type-2 machine. In recursion theory the concept of an “effective Gdel numbering” is fundamental．This number is defined uniquely up to equivalence by the universal turning machine theorem. We generalize the number to notations of the computable functions by means of and the representations of certain continuous functions ，where . This is the presentation and notation of Type-2 machine.