The proof of the existence uncomputable functions in the class of Turing machines is similar to the incompleteness result of Gödel for elementary arithmetic. Since Turing machines were defined to study the notion of computation and thus contain elementary arithmetic. The class of Turing machines is in itself rich enough to express: Universality, Negation and Self-reference. Consequently Turing machines can model universal negative statements about themselves. Turing’s uncomputability proof is al