English

A note reviewing Turing's 1936

Computational Complexity 2025-11-06 v4 Logic in Computer Science

Abstract

By closely rereading the original Turing's 1936 article, we can gain insight about that it is based on the claim to have defined a number which is not computable, arguing that there can be no machine computing the diagonal on the enumeration of the computable sequences. This article provides a careful analysis of Turing's original argument, demonstrating that it cannot be regarded as a conclusive proof. Furthermore, it shows that there is no evidence supporting the existence of a defined number that is not computable.

Keywords

Cite

@article{arxiv.1308.0497,
  title  = {A note reviewing Turing's 1936},
  author = {Paola Cattabriga},
  journal= {arXiv preprint arXiv:1308.0497},
  year   = {2025}
}

Comments

15 pages, for more information see http://paolacattabriga.wordpress.com/

R2 v1 2026-06-22T01:02:56.151Z