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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...

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Published in: Transmathematica
ISSN: 2632-9212
Published: Transmathematica 2020
Online Access: Check full text

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.
Keywords: Fields, Meadows, Rational numbers, Infinity, Errors
College: College of Science
Start Page: 1
End Page: 29