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

• Giovanni Vincenzi ^[1]
  1. [1] Dipartimento di Matematica, Università di Salerno, Fisciano, SA, Italy;Dipartimento di Matematica, Università di Salerno, Fisciano, SA, Italy
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 56, Nº. 1, 2025, págs. 171-177
• Idioma: inglés
• DOI: 10.1080/0020739X.2023.2217690
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• Resumen

  • 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.