English

A definable number which cannot be approximated algorithmically

Computational Complexity 2010-03-03 v1 Logic in Computer Science

Abstract

The Turing machine (TM) and the Church thesis have formalized the concept of computable number, this allowed to display non-computable numbers. This paper defines the concept of number "approachable" by a TM and shows that some (if not all) known non-computable numbers are approachable by TMs. Then an example of a number not approachable by a TM is given.

Keywords

Cite

@article{arxiv.1003.0480,
  title  = {A definable number which cannot be approximated algorithmically},
  author = {Nicolas Brener},
  journal= {arXiv preprint arXiv:1003.0480},
  year   = {2010}
}
R2 v1 2026-06-21T14:52:41.199Z