On the seminal paper written by Einstein, Podolsky and Rosen [1], a critique to the completeness of quantum mechanics was posed. Part of the critique consisted in the following argument: if quantum mechanics is complete, then, two physical quantities, with non-commuting operators, can have simultaneous reality. In this paper I aim to provide a pedagogical approach to the notions used in the EPR's argument. I. INTRODUCTION [...] the best possible knowledge of a whole does not necessarily include the best possible knowledge of all its parts; even though they may be entirely separated and therefore virtually capable of being "best possibly known"[...] E. Schrödinger [2].In 1935, A. Einstein, B. Podoslky and N. Rosen published a paper [1], with a critique to the theory of quantum mechanics. Since then, this paper became a cornerstone when understanding the principles of quantum mechanics is about. In [1], attention was paid to the question of whether quantum mechanics can be a complete theory of physical reality or not. Einstein, Podolsky and Rosen (EPR), clearly emphasized this with the title of the paper:"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?." They claimed that every physical theory, must be complete, and then, according to their analysis, they showed that quantum mechanics is not complete. To show this, they used four criteria, which I describe here as completeness, elements of physical reality, locality and the uncertainty principle.