Is the Halting probability a Dedekind real number?
| dc.creator | Anand, Bhupinder Singh | |
| dc.date | 2003-06-01 | |
| dc.date.accessioned | 2026-07-07T04:58:28Z | |
| dc.date.available | 2026-07-07T04:58:28Z | |
| dc.description | In a recent historical overview, Cristian S. Calude, Elena Calude, and Solomon Marcus identify eight stages in the development of the concept of a mathematical proof in support of an ambitious conjecture: we can express classical mathematical concepts adequately only in a mathematical language in which both truth and provability are essentially unverifiable. In this paper we show, firstly, that the concepts underlying their thesis can, however, be interpreted constructively; and, secondly, that an implicit thesis in the authors' arguments implies that the probability of a given Turing machine halting on a given input cannot be expressed as a Dedekind real number. | |
| dc.description | 32 pages; an HTML version is available at http://alixcomsi.com/index01.htm | |
| dc.identifier | https://arxiv.org/abs/math/0306023 | |
| dc.identifier | http://arxiv.org/abs/math/0306023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67649 | |
| dc.subject | General Mathematics | |
| dc.subject | 03B10 | |
| dc.title | Is the Halting probability a Dedekind real number? | |
| dc.type | text |