Vale para 1, vale para 2, ..., Vale para todos? O Princípio da Indução Finita como instrumento da Matemática na Educação Básica e além.

Abstract

This work aims to treat about an elementary tool for a good understanding of Mathematics, which is the Principle of Finite Induction, unfortunately little used in the teaching of Mathematics in demonstrations in the Primary and Secondary Schools. That principle takes part of the theoretic base foundation of the natural numbers and with it we will certify some properties that involve this numerical set. Almost complete omission of this tool in Primary and Secondary is the motivation of this study, which has object to serve as source for a better understanding of the principle for both students as well for teachers of Primary and Secondary Schools. This work addresses the different formulations of the Principle of Finite Induction and their equivalences. Finally, to reinforce the perception of how this instrument can be used in Primary and Secondary Schools, several examples of properties related to natural numbers are presented, in order to establish a greater affinity with argumentations and demonstrations in a general manner in Mathematics.