The real line and the set of real numbers
Abstract
In this topic we will present an axiomatic definition of the set of real numbers and its properties, distinguishing between algebraic, order and topological axioms or properties. For the latter, the introduction of the concept of the absolute value of a real number will allow us to establish a concept of distance between real numbers and other related notions (environment of a point, points of accumulation, adherence, interior and boundary of a set) that will allow us to complete the description of the real numbers as the set that constitutes the fundamental basis of calculus and mathematical analysis.
References
R. Bartle y D. Sherbert, Introducción al Análisis Matemático de una variable (Ed. Limusa-Noriega, 1996).
M. Protter y C. Morrey, Análisis real (Ed. AC, 1986).
W. Rudin, Principios de Análisis Matemático (Ed. McGraw-Hill, 1976).