Journal article 706 views 92 downloads
The Transrational Numbers as an Abstract Data Type
Jan Aldert Bergstra,
John Tucker 
Transmathematica, Volume: 2020, Pages: 1 - 29
Swansea University Author:
John Tucker
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DOI (Published version): 10.36285/tm.47
Abstract
In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element, such as an error element also denoted with a new constant symbol, an unsigned infinity or one or both signed infinities, one positive and one negative. W...
| Published in: | Transmathematica |
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| ISSN: | 2632-9212 |
| Published: |
Transmathematica
2020
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa56723 |
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| Abstract: |
In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element, such as an error element also denoted with a new constant symbol, an unsigned infinity or one or both signed infinities, one positive and one negative. We define an enlargement of a field to a transfield, in which division is totalised by setting 1/0 equal to the positive infinite value and -1/0 equal to the negative infinite value , and which also contains an error element to help control their effects. We construct the transrational numbers as a transfield of the field of rational numbers and consider it as an abstract data type. We give it an equational specification under initial algebra semantics. |
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| Keywords: |
Fields, Meadows, Rational numbers, Infinity, Errors |
| College: |
Faculty of Science and Engineering |
| Start Page: |
1 |
| End Page: |
29 |