@article{Bergstra_Tucker_2020, title={The Transrational Numbers as an Abstract Data Type}, url={http://transmathematica.org/index.php/journal/article/view/47}, DOI={10.36285/tm.47}, abstractNote={<p>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 its opposite, 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.</p>}, journal={Transmathematica}, author={Bergstra, Jan Aldert and Tucker, John V.}, year={2020}, month={Dec.} }