Why Einstein, Podolsky and Rosen did not prove that quantum mechanics is `incomplete'

It is shown that the Einstein-Podolsky-Rosen conclusion concerning the `incompleteness' of Quantum Mechanics is invalidated by two logical errors in their argument. If it were possible to perform the proposed gedanken experiment it would, in fact, show that Quantum Mechanics is `complete' for the observables discussed. Because, however, of the non square-integrable nature of the wave function, the proposed experiment gives vanishing probabilities for measurements performed in finite intervals of configuration or momentum space. Hence no conclusion as to the `completeness', or otherwise, of Quantum Mechanics can be drawn from the experiment.