Zenbaki errealak eraikitzen
ISSN: 0214-9001
Year of publication: 2016
Issue: 29
Pages: 107-125
Type: Article
More publications in: Ekaia: Euskal Herriko Unibertsitateko zientzi eta teknologi aldizkaria
Abstract
Even though real numbers are such an important tool and model in mathematics, no strict description is provided in many situations. The aim of this paper is to fill this gap by presenting some of these constructions. After giving a synthetic definition of the real numbers and a precise definition of rational numbers, we present the classical constructions of the real numbers proposed by Cantor, Dedekind and Weierstrass. Indeed, these were the first successful descriptions of the field of the real numbers. Finally, we explain the definition given by Rota and three other mathematicians, showing that this work can also be carried out by an algebraic approach.