Les extensions intrinseques les plus simples des ensembles R et N pour une nouvelle Analyse Non standard

TL;DR

This paper introduces simple intrinsic extensions of the sets of non-negative integers and real numbers, providing a new form of Non-Standard Analysis with formal constructions and comparisons to existing NSA frameworks.

Contribution

It presents novel intrinsic extensions of N and R, along with the first differential and integral elements in a simplified NSA* framework, contrasting it with established NSA theories.

Findings

Constructed the Aleph intrinsic extension of N.

Defined the Omega smallest strict over-field of R.

Compared NSA* with Robinson's and Conway's NSA.

Abstract

The main results of this paper are the formal constructions, both rigorous and intuitive of the "Aleph" intrinsic extension of the set of non negative integers N and the "Omega" smallest strict over-field of R which is totally ordered and complete. The first differential and integral elements of a new Non Standard Analysis (NSA*) are given. This very simple NSA* is compared to A.Robinson's and J.H.Conway's.