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| Format: | Preprint |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1308.0497 |
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| _version_ | 1866912687939649536 |
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| author | Cattabriga, Paola |
| author_facet | Cattabriga, Paola |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1308_0497 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | A note reviewing Turing's 1936 Cattabriga, Paola Computational Complexity Logic in Computer Science 03D10, 68Qxx 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. |
| title | A note reviewing Turing's 1936 |
| topic | Computational Complexity Logic in Computer Science 03D10, 68Qxx |
| url | https://arxiv.org/abs/1308.0497 |