A geometric interpretation of the Peano Axioms as a didactic strategy for teaching and learning natural numbers Una interpretación geométrica de los Axiomas de Peano como estrategia didáctica para la enseñanza y aprendizaje de los números naturales

Abstract

Peano’s axioms are a set of propositions that allow a formal definition of the set of natural numbers. In these axioms, Peano rescues the essence of counting objects and materializes it by assuming the existence of a set, of a function in this set (which he calls successor) and an axiom of induction. In this work a geometrical representation and interpretation of each of these axioms is made, which allows understanding the independence and necessity of each one of them, which facilitates giving the conceptual rigor of them by making use of mathematical language. Finally, using Euclidean geometry, a geometric construction of a system of natural numbers on a straight line is made.