Back إنشاء الأعداد الحقيقية Arabic Construcció dels nombres reals Catalan Axiomas de los números reales Spanish Construction des nombres réels French בניית המספרים הממשיים HE Konstruksi bilangan real ID Costruzione dei numeri reali Italian 실수의 구성 Korean Конструктивные способы определения вещественного числа Russian 實數的構造 Chinese
In mathematics, there are several equivalent ways of defining the real numbers. One of them is that they form a complete ordered field that does not contain any smaller complete ordered field. Such a definition does not prove that such a complete ordered field exists, and the existence proof consists of constructing a mathematical structure that satisfies the definition.
The article presents several such constructions.[1] They are equivalent in the sense that, given the result of any two such constructions, there is a unique isomorphism of ordered field between them. This results from the above definition and is independent of particular constructions. These isomorphisms allow identifying the results of the constructions, and, in practice, to forget which construction has been chosen.