Transreal Integral

Authors

  • Tiago Soares dos Reis Federal Institute of Education, Science and Technology of Rio de Janeiro

DOI:

https://doi.org/10.36285/tm.v0i0.13

Abstract

This paper improves an early approach and defines an integral on transreal numbers which extends the usual integral on real numbers. The present integral works on transreal numbers and integrates all functions which are properly or improperly integrable, in the usual sense, on real numbers.

References

J. A. D. W. Anderson and T. S. dos Reis. “Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics.” Accessed on 8 April 2019. Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering and Computer Science 2014, WCECS 2014, 22-24 October, 2014,San Francisco, USA., pp. 86-91.

T. S. dos Reis. “Proper and improper Riemann integral in a single definition.” Accessed on 8 April 2019. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics. 5, pp.010017-1–010017-7, 2016.

T. S. dos Reis and J. A. D. W. Anderson. “Transdifferential and transintegral calculus.” Accessed on 8 April 2019. Lecture Notes in Engineering and Computer Science: Proceedings of The World Congresson Engineering and Computer Science 2014, WCECS 2014, 22-24 October, 2014, San Francisco, USA., pp. 92–96.

T. S. dos Reis and J. A. D. W. Anderson. “Transreal limits and elementary functions.” Accessed on 8 April 2019. Transactions on Engineering Technologies – World Congress on Engineering and Computer Science 2014, pp. 209–225.

T. S. dos Reis and J. A. D. W. Anderson. “Transreal calculus.” Accessed on 8 April 2019. IAENG International Journal of Applied Mathematics, 45(1), pp. 51–63, 2015.

T. S. dos Reis, W. Gomide, and J. A. D. W. Anderson. “Construction of the transreal numbers and algebraic transfields.” Accessed on 8 April 2019. IAENG International Journal of Applied Mathematics, 46(1), pp. 11–23, 2016.

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Published

2019-06-25

How to Cite

Reis, T. S. dos. (2019). Transreal Integral. Transmathematica. https://doi.org/10.36285/tm.v0i0.13

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Section

Primary Article