An elementary exposition of Gödel's incompleteness theorem

Godel's incompleteness theorem states that there is no system of axioms and rules of inference such that the totality of all assertions deducible from the axioms is the same as the totality of all true assertions in arithmetic (indeed, for every consistent system one can construct effectively a true but unprovable assertion). The present article is devoted to a proof of this theorem, based on the concepts and methods of the theory of algorithms; the necessary information from the theory of algorithms is provided. The paper does not require specialized knowledge of any kind (in particular, none from mathematical logic), but assumes only a familiarity with elementary mathematical terminology and symbolism.