Characteristic Numbers Whose Divisor Approaches Zero

Emerson Freitas Jaguaribe

doi:https://doi.org/10.14445/22315373/IJMTT-V72I5P112

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 5 | Year 2026 | Article Id. IJMTT-V72I5P112 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I5P112

Characteristic Numbers Whose Divisor Approaches Zero

Emerson Freitas Jaguaribe

Received	Revised	Accepted	Published
03 Apr 2026	04 May 2026	19 May 2026	30 May 2026

Citation :

Emerson Freitas Jaguaribe, "Characteristic Numbers Whose Divisor Approaches Zero," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 5, pp. 125-133, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I5P112

Abstract

Historical records have examined the origins and significance of zero, yet a fundamental question remains unanswered: What is the value of a/0, where a can be either zero or a non-zero value? Brahmagupta and Bhaskara, two prominent Indian mathematicians, held opposing views on this issue, but neither offered a definitive solution. Various attempts to address this problem—such as introducing new symbols to expand the set of real numbers, applying proposed transreal analysis, utilizing stereographic projection, or employing the sgn function—have proven unsuccessful. The reality is that treating a/0 in isolation does not make sense. A meaningful natural process to elucidate this problem requires the quotients to appear as characteristic numbers. In conformity with the use of applied mathematics and real life, it is necessary to recognize that no natural process involves a zero denominator. This work, illustrated with experimental examples, shows that when the denominator of a quotient approaches zero, using characteristic numbers associated with the limit of that quotient yields finite results, intervening in the definition of infinity. This approach facilitates the management of potential hardware exceptions and helps programmers develop more efficient software to prevent division-by-zero errors.

Keywords

Aristotle’s Theory on Natural Motion, Bhramagupta’s and Bhaskara’s 0/0, Characteristic Number, Division by Zero and Infinity, Solar Radiation Amplification using a Truncate Cone Mirror.

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