International Journal of Mathematics Trends and Technology
Volume 71 | Issue 1 | Year 2025 | Article Id. IJMTT-V71I1P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I1P102
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 12 Nov 2024 | 26 Dec 2024 | 10 Jan 2025 | 30 Jan 2025 |
Division by Zero is traditionally undefined in standard arithmetic due to its inherent contradictions. This paper presents a novel algebraic framework that redefines arithmetic operations using Boolean-like operations: OR for Addition, XNOR for Multiplication and Complex numbers or XOR as an exception to certain cases of distributivity. By leveraging these operations, a consistent system is developed that allows for the definition of Division by Zero, at least within a Binary Set, and this framework is extended to Real numbers. This new approach opens potential applications in theoretical mathematics, logic, computer technology and many other fields of science.
Abelian group, Boolean algebra, Division by zero, Fuzzy logic, Real numbers.
[1] Examples.com Website, Admin, 2024. [Online]. Available: https://www.examples.com/maths/boolean-algebra.html
[2] CTAN Website, CTAN: Join the CTAN Community, 2024. [Online]. Available: https://ctan.org/join?lang=en
[3] Zhongfei Zhang, and Ruofei Zhang, Multimedia Data Mining - A Systematic Introduction to Concepts and Theory, Chapman and
Hall/CRC, New York, 1st ed., 2008.
[CrossRef] [Google Scholar] [Publisher Link]
[4] Boolean Algebra, Italian IT-Training Website, 2024. [Online]. Available:
https://www.classicistranieri.com/it/a/l/g/Algebra_di_Boole_72d9.html
[5] Italian-Language Edition of Wikipedia, Wikimedia Foundation, 2024. [Online]. Available:
https://en.wikipedia.org/wiki/Italian_Wikipedia
[6] Compendium on XOR in Programming, 2024. [Online]. Available:
https://forums.cncnet.org/topic/2318-introduction-to-moddinghacking/
[7] Jorgeluisorejel, Generic XOR-Coded Lists, Codeproject, 2024. [Online]. Available:
https://www.codeproject.com/Articles/1083211/Generic-XOR-Coded-Lists
[8] French Website on Group Abilities of XNOR, 2024. [no longer online, but still indexed]. [Online]. Available:
http://www.arcanapercipio.com/techno/boole.php
Till Meyenburg, "A Novel Algebraic Framework for Division by Zero Using Boolean Operations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 1, pp. 8-15, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I1P102
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