More Theory About Infinite Numbers and Important Applications
In the author’s previous studies, new infinite numbers, their properties, and calculations were introduced. These infinite numbers quantify infinity and offer new possibilities for solving complicated problems in mathematics and applied sciences in which infinity appears. The current study presents...
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MDPI AG
2025-04-01
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| Series: | Mathematics |
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| author | Emmanuel Thalassinakis |
| author_facet | Emmanuel Thalassinakis |
| author_sort | Emmanuel Thalassinakis |
| collection | DOAJ |
| description | In the author’s previous studies, new infinite numbers, their properties, and calculations were introduced. These infinite numbers quantify infinity and offer new possibilities for solving complicated problems in mathematics and applied sciences in which infinity appears. The current study presents additional properties and topics regarding infinite numbers, as well as a comparison between infinite numbers. In this way, complex problems with inequalities involving series of numbers, in addition to limits of functions of <i>x</i> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>∈</mo></semantics></math></inline-formula> ℝ and improper integrals, can be addressed and solved easily. Furthermore, this study introduces rotational infinite numbers. These are not single numbers but sets of infinite numbers produced as the vectors of ordinary infinite numbers are rotated in the complex plane. Some properties of rotational infinite numbers and their calculations are presented. The rotational infinity unit, its inverse, and its opposite number, as well as the angular velocity of rotational infinite numbers, are defined and illustrated. Based on the above, the Riemann zeta function is equivalently written as the sum of three rotational infinite numbers, and it is further investigated and analyzed from another point of view. Furthermore, this study reveals and proves interesting formulas relating to the Riemann zeta function that can elegantly and simply calculate complicated ratios of infinite series of numbers. Finally, the above theoretical results were verified by a computational numerical simulation, which confirms the correctness of the analytical results. In summary, rotational infinite numbers can be used to easily analyze and solve problems that are difficult or impossible to solve using other methods. |
| format | Article |
| id | doaj-art-e4394bf35a324c89879c86c072a1fb24 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-e4394bf35a324c89879c86c072a1fb242025-08-20T01:49:11ZengMDPI AGMathematics2227-73902025-04-01139139010.3390/math13091390More Theory About Infinite Numbers and Important ApplicationsEmmanuel Thalassinakis0Applied Mathematics and Computers Laboratory (AMCL), Technical University of Crete, Akrotiri Campus, 73100 Chania, GreeceIn the author’s previous studies, new infinite numbers, their properties, and calculations were introduced. These infinite numbers quantify infinity and offer new possibilities for solving complicated problems in mathematics and applied sciences in which infinity appears. The current study presents additional properties and topics regarding infinite numbers, as well as a comparison between infinite numbers. In this way, complex problems with inequalities involving series of numbers, in addition to limits of functions of <i>x</i> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>∈</mo></semantics></math></inline-formula> ℝ and improper integrals, can be addressed and solved easily. Furthermore, this study introduces rotational infinite numbers. These are not single numbers but sets of infinite numbers produced as the vectors of ordinary infinite numbers are rotated in the complex plane. Some properties of rotational infinite numbers and their calculations are presented. The rotational infinity unit, its inverse, and its opposite number, as well as the angular velocity of rotational infinite numbers, are defined and illustrated. Based on the above, the Riemann zeta function is equivalently written as the sum of three rotational infinite numbers, and it is further investigated and analyzed from another point of view. Furthermore, this study reveals and proves interesting formulas relating to the Riemann zeta function that can elegantly and simply calculate complicated ratios of infinite series of numbers. Finally, the above theoretical results were verified by a computational numerical simulation, which confirms the correctness of the analytical results. In summary, rotational infinite numbers can be used to easily analyze and solve problems that are difficult or impossible to solve using other methods.https://www.mdpi.com/2227-7390/13/9/1390infinityinfinite numbersrotational infinite numbersgraphical representationvectorscomplex numbers |
| spellingShingle | Emmanuel Thalassinakis More Theory About Infinite Numbers and Important Applications Mathematics infinity infinite numbers rotational infinite numbers graphical representation vectors complex numbers |
| title | More Theory About Infinite Numbers and Important Applications |
| title_full | More Theory About Infinite Numbers and Important Applications |
| title_fullStr | More Theory About Infinite Numbers and Important Applications |
| title_full_unstemmed | More Theory About Infinite Numbers and Important Applications |
| title_short | More Theory About Infinite Numbers and Important Applications |
| title_sort | more theory about infinite numbers and important applications |
| topic | infinity infinite numbers rotational infinite numbers graphical representation vectors complex numbers |
| url | https://www.mdpi.com/2227-7390/13/9/1390 |
| work_keys_str_mv | AT emmanuelthalassinakis moretheoryaboutinfinitenumbersandimportantapplications |