Una costruzione del sistema dei numeri reali

TL;DR

This paper presents a clear and rigorous construction of the real numbers from positive rationals using initial segments, offering an alternative to traditional methods like Cauchy sequences and Dedekind cuts.

Contribution

It introduces a novel construction of the real numbers based on initial segments of positive rationals, simplifying and clarifying the process.

Findings

Provides a rigorous construction method for real numbers

Simplifies the understanding of real number construction

Offers an alternative to traditional methods

Abstract

There are many ways to construct the field R of real numbers. The most important and famous of these employ Cauchy sequences (Cantor) or cuts (Dedekind) in the field Q of rational numbers. These constructions sometimes overlook important details and often are complicated and cumbersome. In this note, the authors propose an essential, clear and rigorous construction of R from the stucture Q+ of positive rational numbers by the key notion of initial segment.