Inconsistency of ℕ

The graphical-geometrical representation of ℕ, and hence of actual infinity, requires the existence of infinitesimal intervals. However, such intervals do not exist when the representation is based on the rational numbers.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-25
DOI
https://doi.org/10.5281/zenodo.22101977
Primary Topic
Mathematical and Theoretical Analysis
Type
preprint
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preprint

Inconsistency of ℕ

Enrico Pier Giorgio Cadeddu
Zenodo (CERN European Organization for Nuclear Research)
Mathematical and Theoretical Analysis
preprint

Inconsistency of ℕ

Enrico Pier Giorgio Cadeddu
preprint en

Abstract

The graphical-geometrical representation of ℕ, and hence of actual infinity, requires the existence of infinitesimal intervals. However, such intervals do not exist when the representation is based on the rational numbers.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Mathematical and Theoretical Analysis
DOIOpen Access PDFOpenAlex
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Inconsistency of ℕ — Enrico Pier Giorgio Cadeddu · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS