PRIMEIRO PRINCÍPIO DA INDUÇÃO E O PRINCÍPIO DA BOA ORDENAÇÃO: APLICAÇÕES E EQUIVALÊNCIA

Abstract

Mathematical problems involving properties related to numerical sets are common in mathematics competitions, such as the Brazilian Public School Mathematics Olympiad (OBMEP). In this perspective, the authors' participation in the Junior Scientific Initiation Program of OBMEP - PIC OBMEP at Vale do Acaraú State University (UVA) and the routine exposure to problems fitting the description above stimulate the desire to investigate, in a more qualitative manner, some of the tools used to solve such problems. Therefore, the present work aims to state and demonstrate some properties related to natural numbers, taking the Principle of Finite Induction (PFI) and the Principle of Well-Ordering (PWO) as the main demonstration tools, as well as the equivalence between these principles.