Bagaria, JoanReverté Jorge, Mercè2023-10-272023-10-272023-06-12https://hdl.handle.net/2445/203201Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Joan Bagaria[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.54 p.application/pdfcatcc-by-nc-nd (c) Mercè Reverté Jorge, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Teoria de conjuntsLògica matemàticaNombres realsTreballs de fi de grauSet theoryMathematical logicReal numbersBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess