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Construction of the transcomplex numbers from the complex numbers

dos Reis, T. S. and Anderson, J. A.D.W. (2014) Construction of the transcomplex numbers from the complex numbers. In: International Conference on Computer Science and Applications (WCECS 2014), 22-24 October 2014, San Francisco, USA,, pp. 97-102.

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A geometrical construction of the transcomplex numbers was given elsewhere. Here we simplify the transcomplex plane and construct the set of transcomplex numbers from the set of complex numbers. Thus transcomplex numbers and their arithmetic arise as consequences of their construction, not by an axiomatic development. This simplifes transcom- plex arithmetic, compared to the previous treatment, but retains totality so that every arithmetical operation can be applied to any transcomplex number(s) such that the result is a transcomplex number. Our proof establishes the consistency of transcomplex and transreal arithmetic and establishes the expected containment relationships amongst transcomplex, complex, transreal and real numbers. We discuss some of the advantages the transarithmetics have over their partial counterparts.

Item Type:Conference or Workshop Item (Paper)
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Computer Science
ID Code:37402
Uncontrolled Keywords:transcomplex numbers, transcomplex arithmetic, transreal numbers, transreal arithmetic
Additional Information:Proceedings: World Congress on Engineering and Computer Science 2014, San Francisco, USA, 22-24 October, 2014 Publisher: International Association of Engineers Pages: 97-102 ISBN: 9789881925 ISSN: 2078-0958


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