Intuição matemática

Abstract

In this paper, we present several interesting mathematical facts, which show that we should not rely solely on our intuition. This theme relates to a relatively new area of mathematics called Lineability. This area seeks the existence of large mathematical structures, which are composed of objects with certain “pathological” properties. After explaining the prerequi- sites and basic concepts about this theory, which deal in their breadth with Cardinality and Finite and Infinite Dimensional Vector Spaces, some examples and Lineability properties are discussed in sequence and functions spaces. This research is of bibliographic and qualita- tive nature, as it seeks to interpret and analyze the facts that happened during the episodes fomented in the investigations of authors that address the theme and for involving questions related to the teaching of mathematics. As for data collection instruments, we use only the contribution of articles and theses contained in databases, annotations and written records. Therefore, the study shows that working with intuition-inspiring classes and mathematical activities focused on this contexts provide new opportunities for students to develop and dis- seminate their mathematical ideas in the classroom.