A new kind of numbers, the Non-Dedekindian Numbers, and the extension to them of the notion of algorithmic randomness
| dc.creator | Segre, Gavriel | |
| dc.date | 2006-12-20 | |
| dc.date | 2007-01-08 | |
| dc.date.accessioned | 2026-07-07T07:38:49Z | |
| dc.date.available | 2026-07-07T07:38:49Z | |
| dc.description | A new number system, the set of the non-Dedekindian numbers, is introduced and characterized axiomatically. It is then proved that any hypercontinous hyperreal number system is strictly included in the set of the Non-Dedekindian Numbers. The notion of algorithmic-randomness is then extended to non-Dedekindian numbers. As a particular case, the notion of algorithmic randomness for the particular hyperreal number system of Non-Standard Analysis is explicitly analyzed. | |
| dc.description | The third version differs from the second version in the correction of some lapses | |
| dc.identifier | https://arxiv.org/abs/math/0612590 | |
| dc.identifier | http://arxiv.org/abs/math/0612590 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121230 | |
| dc.subject | General Mathematics | |
| dc.title | A new kind of numbers, the Non-Dedekindian Numbers, and the extension to them of the notion of algorithmic randomness | |
| dc.type | text |