In this special episode we have a guest mathematician. Gabriel Barrenechea joins us talking about sequences, convergence and completeness. We identify the last remaining axiom we need to uniquely identify the real numbers. Asking for completeness, that is, any Cauchy sequence is supposed to converge, we provide a means to fill the holes of the rationals. With this property we can show existence of square roots of any positive number, which will be done in the next chapter.