Construcció dels nombres reals: estructura i propietats del continu

Abstract

[en] The linear continuum is a mathematical object of great importance. In this project we give a construction of the real numbers, a particular linear continuum, starting with the natural numbers and using basic notions of set theory. We briefly discuss the set of real numbers as a complete ordered field. Finally, we present some of its regularity properties under ZFC, where we also see the existence of pathological sets of real numbers that don’t satisfy said properties.