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Transreal calculus

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dos Reis, T. S. and Anderson, J. (2015) Transreal calculus. IAENG International Journal of Applied Mathematics, 45 (1). pp. 51-63. ISSN 1992-9986

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Official URL: http://www.iaeng.org/IJAM/issues_v45/issue_1/index...

Abstract/Summary

Transreal arithmetic totalises real arithmetic by defining division by zero in terms of three definite, non-finite numbers: positive infinity, negative infinity and nullity. We describe the transreal tangent function and extend continuity and limits from the real domain to the transreal domain. With this preparation, we extend the real derivative to the transreal derivative and extend proper integration from the real domain to the transreal domain. Further, we extend improper integration of absolutely convergent functions from the real domain to the transreal domain. This demonstrates that transreal calculus contains real calculus and operates at singularities where real calculus fails.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Computer Science
ID Code:39280
Uncontrolled Keywords:transreal arithmetic, transreal tangent, transreal continuity, transreal limit, transreal derivative, transreal integral, transreal calculus.
Publisher:International Association of Engineers

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