El teorema de Bolzano

Abstract

[en] Bolzano’s theorem is indisputably a classic theorem in mathematical analysis. In this work we present its mathematical construction with its many applications, from the simple location of roots to numerical methods based on this result. I dedicate a section in addition to its possible generalizations where we will analyze Bolzano’s theorem topologically. Finally I will propose a didactic part where we will see how to carry this theorem in the classroom and work on the mathematical language, an essential element in mathematics.