### Santilli Isomathematics for Generalizing Modern Mathematics

Received: 2 June 2015    Accepted: 2 June 2015    Published: 11 August 2015
Abstract

The establishment of isomathematics, as proposed by R. M. Santilli thirty years ago in the USA, and contributed to by Jiang Chun-Xuan in China during the past 12 years, is significant and has changed modern mathematics. At present, the primary teaching of mathematics is based on the simple operations of addition, subtraction, multiplication and division; a middle level teaching ofmathematics takes these four operations to a higher level, while the university teaching of mathematics extends them to an even higher level. These four arithmetic operations form the foundation of modern mathematics. Santilli isomathematics is a generalisation of these four fundamental operations and heralds a great revolution in mathematics. HIn this paper, we study the four generalized arithmetic operations of isoaddition, isosubtraction, isomultiplication and isodivision at the primary level of isomathematics. The material introduced here should be readily understandable by middle school pupils and university students.Santilli’s isomathematics [1] ßßis based on a generalisation of modern mathematics. Isomultiplication is defined by a× ̂a=abT ̂, isodivision by a÷ ̂b=a/b I ̂, where I ̂≠1 is called an isounit; T ̂I ̂=1, where T ̂ is the inverse of the isounit. If addition and subtraction remain unchanged, (+ ̂,- ̂,× ̂,÷ ̂)are the four arithmetic operations in Santilli’s isomathematics[1-5]. Isoaddition a+ ̂b=a+b+0 ̂ and isosubtraction a+ ̂b=a+b+0 ̂, where 0 ̂≠0 is called the isozero, together with the operations of isomultiplication and isodivision introduced above, form the four arithmetic operations(+ ̂,- ̂,× ̂,÷ ̂) in Santilli-Jiang isomathematics[6]. Santilli [1] suggests isomathematics based on a generalisation of multiplication ×, division ÷, and the multiplicative unit 1 of modern mathematics. It is an epoch making suggestion. From modern mathematics, the foundations of Santilli’s isomathematics will be established

Keywords

References
 [1] R. M. Santilli, Rendiconti Circolo Matematico Palermo, Suppl. Vol. 42, 7-82 (1996),\\ http://www.santilli-foundation.org/docs/Santilli-37.pdf [2] Chun-Xuan Jiang, (1998), Foundations of Santilli’s isonumber theory, Part I: Isonumber theory of the first kind; Algebras, Groups and Geometries, 15, 351-393. [3] Chun-Xuan Jiang, (1998), Foundations of Santilli’s isonumber theory, Part II: Isonumber theory of the second kind; Algebras Groups and Geometries, 15, 509-544. [4] Chun-Xuan Jiang, (1999), Foundations of Santilli’s isonumber theory, in: Fundamental open problems in sciences at the end of the millennium, T. Gill, K. Liu and E. Trell (Eds), Hadronic Press, USA, 105-139. [5] Chun-Xuan Jiang, (2002), Foundations of Santilli’s isonumber theory, with applications to new cryptograms, Fermat’s theorem and Goldbach’s conjecture, International Academic Press, America- Europe- Asia.MR2004c:11001. (also available in the pdf file http: // www. i-b-r. org/docs/jiang.pdf) (http://vixra.org/pdf/1303.0088v1.pdf)) [6] Chun-Xuan Jiang,(2008),Santilli-Jiang isomathematics for changing modern mathematics,middle school mathematics(Chinese),Dec.46-48
• APA Style

Chun-Xuan Jiang. (2015). Santilli Isomathematics for Generalizing Modern Mathematics. American Journal of Modern Physics, 4(5-1), 35-37. https://doi.org/10.11648/j.ajmp.s.2015040501.14

ACS Style

Chun-Xuan Jiang. Santilli Isomathematics for Generalizing Modern Mathematics. Am. J. Mod. Phys. 2015, 4(5-1), 35-37. doi: 10.11648/j.ajmp.s.2015040501.14

AMA Style

Chun-Xuan Jiang. Santilli Isomathematics for Generalizing Modern Mathematics. Am J Mod Phys. 2015;4(5-1):35-37. doi: 10.11648/j.ajmp.s.2015040501.14

• ```@article{10.11648/j.ajmp.s.2015040501.14,
author = {Chun-Xuan Jiang},
title = {Santilli Isomathematics for Generalizing Modern Mathematics},
journal = {American Journal of Modern Physics},
volume = {4},
number = {5-1},
pages = {35-37},
doi = {10.11648/j.ajmp.s.2015040501.14},
url = {https://doi.org/10.11648/j.ajmp.s.2015040501.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.s.2015040501.14},
abstract = {The establishment of isomathematics, as proposed by R. M. Santilli thirty years ago in the USA, and contributed to by Jiang Chun-Xuan in China during the past 12 years, is significant and has changed modern mathematics. At present, the primary teaching of mathematics is based on the simple operations of addition, subtraction, multiplication and division; a middle level teaching ofmathematics takes these four operations to a higher level, while the university teaching of mathematics extends them to an even higher level. These four arithmetic operations form the foundation of modern mathematics. Santilli isomathematics is a generalisation of these four fundamental operations and heralds a great revolution in mathematics. HIn this paper, we study the four generalized arithmetic operations of isoaddition, isosubtraction, isomultiplication and isodivision at the primary level of isomathematics. The material introduced here should be readily understandable by middle school pupils and university students.Santilli’s isomathematics [1] ßßis based on a generalisation of modern mathematics. Isomultiplication is defined by a× ̂a=abT ̂, isodivision by  a÷ ̂b=a/b I ̂, where I ̂≠1 is called an isounit; T ̂I ̂=1, where T ̂ is the inverse of the isounit. If addition and subtraction remain unchanged, (+ ̂,- ̂,× ̂,÷ ̂)are the four arithmetic operations in Santilli’s isomathematics[1-5]. Isoaddition a+ ̂b=a+b+0 ̂ and isosubtraction a+ ̂b=a+b+0 ̂, where 0 ̂≠0 is called the isozero, together with the operations of isomultiplication and isodivision introduced above, form the four arithmetic operations(+ ̂,- ̂,× ̂,÷ ̂) in Santilli-Jiang isomathematics[6]. Santilli [1] suggests isomathematics based on a generalisation of multiplication ×, division ÷, and the multiplicative unit 1 of modern mathematics. It is an epoch making suggestion. From modern mathematics, the foundations of Santilli’s isomathematics will be established},
year = {2015}
}
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VL  - 4
IS  - 5-1
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Author Information
• Institute for Basic Research, Beijing, P. R. China

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