Irrationality via base-<italic>b</italic> representation: an alternative proof of Gauss's lemma.

Using the basic properties of the base-<italic>b</italic> representation of rational numbers, we will give an elementary proof of Gauss's lemma: <italic>Every real root of a monic polynomial with integer coefficients is either an integer or irrational</italic>. The paper offers a new perspective in understanding the meaning of ‘irrational numbers’ from a deeper perspective, and a good occasion to improve the student's skills with point of view on number systems. [ABSTRACT FROM AUTHOR]