Introdução à lógica matemática com aplicações na educação básica

Abstract

This work aims to present an introduction to the Logic used in the development of the Axiomatic Theories associated with the Basic Education Mathematics Curriculum according to the Common National Curriculum Basis. Emphasis is given to the discussion of the most used demonstration methods to justify the main mathematical results presented at this level. It highlights, among others, the Methods of Demonstration by Direct Proof, Reduction to Absurdity and Mathematical Induction, which, unlike most of the literature, presents the entire relationship of these methods with Logic, its principles, operations and inference rules prerequisites justification for their use is fundamental. In particular, it makes a more comprehensive discussion of the Mathematical Induction Method associating it both to the Principle or Axiom of Induction and to the Induction Theorem, demonstrating it and presenting its various applications whether in the rigorous definition of mathematical objects or as a powerful instrument to demonstrate the most varied results involving natural numbers in basic education. In addition, it brings examples of Axiomatic Theories developed at this level and enunciates several Theorems making their respective demonstrations using one or more of the demonstration methods presented including the demonstration in standard argument notation,thus explaining its direct relationship with logic and its algebra. The work can be used as a support material for the teacher of basic education or graduating from a Mathematics Degree Course who wishes to go deeper in what concerns the Techniques of Demonstration of Theorems and all the Logic behind these processes.