Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: Every real root of a monic polynomial with integer coefficients is either an integer or irrational. 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.

Irrationality via base-b representation: an alternative proof of Gauss's lemma

Vincenzi, Giovanni
2023-01-01

Abstract

Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: Every real root of a monic polynomial with integer coefficients is either an integer or irrational. 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4883231
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