Una costruzione del sistema dei numeri reali
Maria Rosaria Enea, Donato Saeli

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.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Computability, Logic, AI Algorithms
