A NOVEL CONCEPT: THE PRODUCT OF TWO NEGATIVELY DIRECTED NUMBERS IS A NEGATIVELY DIRECTED NUMBER THOUGH THE NEGATIVE OF A NEGATIVE NUMBER IS A POSITIVE NUMBER
In this paper, the author proved that the product of two negatively directed numbers is a negatively directed number. This article is the outcome of previously published (2021-2024) ten (10) articles of this author. It is true that the negative of a negative number is a positive number. It has been...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mechanics of Continua and Mathematical Sciences
2024-10-01
|
| Series: | Journal of Mechanics of Continua and Mathematical Sciences |
| Subjects: | |
| Online Access: | https://jmcms.s3.amazonaws.com/wp-content/uploads/2024/10/10060129/jmcms-2409031-Negatively-Directed-Numbers-PCB.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849387959492542464 |
|---|---|
| author | Prabir Chandra Bhattacharyya |
| author_facet | Prabir Chandra Bhattacharyya |
| author_sort | Prabir Chandra Bhattacharyya |
| collection | DOAJ |
| description | In this paper, the author proved that the product of two negatively directed
numbers is a negatively directed number. This article is the outcome of previously published (2021-2024) ten (10) articles of this author. It is true that the negative of a negative number is a positive number. It has been done by applying the inversion process to a negative number. The process of inversion does not satisfy the basic concept of multiplication. Multiplication is defined as the adding of a number concerning another number repeatedly. So, the process of inversion does not comply with the fundamental concept of multiplication. According to the Theory of Dynamics of Numbers there exist three types of numbers: (1) Neutral or discrete numbers (2)Positively directed numbers (3) Negatively directed numbers. In general, we use four types of operators: addition (+), subtraction (-), multiplication (x), and division (÷) in mathematical calculations. Besides these, we use the negative sign (-) as an inversion operator. The positive sign (+) and negative sign (-) also represent the direction of neutral or discrete numbers. In this paper, the author introduced Fermat's Last Theorem: xn + yn = znfor n = 2 in Bhattacharyya's Theorem to prove that the product of two negatively directed numbers is a negatively directed number using the concept
of the Theory of Dynamics of Numbers. In this paper, the author framed new laws of multiplication and inversion. Also, the author has given a comparative study between the conventional method of multiplication and the present concept of multiplication citing some practical examples. The author has become successful in finding the root of a quadratic equation in real numbers even if the discriminant, b2– 4ac < 0 without using the concept of the imaginary number and also in determining the radius of a circle even if g2 + f2 < c, in real number without using the concept of complex numbers. With one example the author proved that this theorem is applicable in ‘Calculus’ also. |
| format | Article |
| id | doaj-art-fac4d11d42804041a82b4aa88806992e |
| institution | Kabale University |
| issn | 0973-8975 2454-7190 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Institute of Mechanics of Continua and Mathematical Sciences |
| record_format | Article |
| series | Journal of Mechanics of Continua and Mathematical Sciences |
| spelling | doaj-art-fac4d11d42804041a82b4aa88806992e2025-08-20T03:42:26ZengInstitute of Mechanics of Continua and Mathematical SciencesJournal of Mechanics of Continua and Mathematical Sciences0973-89752454-71902024-10-01191011810.26782/jmcms.2024.10.00001A NOVEL CONCEPT: THE PRODUCT OF TWO NEGATIVELY DIRECTED NUMBERS IS A NEGATIVELY DIRECTED NUMBER THOUGH THE NEGATIVE OF A NEGATIVE NUMBER IS A POSITIVE NUMBERPrabir Chandra Bhattacharyya0Department of Mathematics, Institute of Mechanics of Continua and Mathematical Sciences. Madhyamgram, Kolkata, India.In this paper, the author proved that the product of two negatively directed numbers is a negatively directed number. This article is the outcome of previously published (2021-2024) ten (10) articles of this author. It is true that the negative of a negative number is a positive number. It has been done by applying the inversion process to a negative number. The process of inversion does not satisfy the basic concept of multiplication. Multiplication is defined as the adding of a number concerning another number repeatedly. So, the process of inversion does not comply with the fundamental concept of multiplication. According to the Theory of Dynamics of Numbers there exist three types of numbers: (1) Neutral or discrete numbers (2)Positively directed numbers (3) Negatively directed numbers. In general, we use four types of operators: addition (+), subtraction (-), multiplication (x), and division (÷) in mathematical calculations. Besides these, we use the negative sign (-) as an inversion operator. The positive sign (+) and negative sign (-) also represent the direction of neutral or discrete numbers. In this paper, the author introduced Fermat's Last Theorem: xn + yn = znfor n = 2 in Bhattacharyya's Theorem to prove that the product of two negatively directed numbers is a negatively directed number using the concept of the Theory of Dynamics of Numbers. In this paper, the author framed new laws of multiplication and inversion. Also, the author has given a comparative study between the conventional method of multiplication and the present concept of multiplication citing some practical examples. The author has become successful in finding the root of a quadratic equation in real numbers even if the discriminant, b2– 4ac < 0 without using the concept of the imaginary number and also in determining the radius of a circle even if g2 + f2 < c, in real number without using the concept of complex numbers. With one example the author proved that this theorem is applicable in ‘Calculus’ also.https://jmcms.s3.amazonaws.com/wp-content/uploads/2024/10/10060129/jmcms-2409031-Negatively-Directed-Numbers-PCB.pdfbhattacharyya's theoremconcept of limitnumber theoryrectangular bhattacharyya's coordinatesrole of multiplication and inversion |
| spellingShingle | Prabir Chandra Bhattacharyya A NOVEL CONCEPT: THE PRODUCT OF TWO NEGATIVELY DIRECTED NUMBERS IS A NEGATIVELY DIRECTED NUMBER THOUGH THE NEGATIVE OF A NEGATIVE NUMBER IS A POSITIVE NUMBER Journal of Mechanics of Continua and Mathematical Sciences bhattacharyya's theorem concept of limit number theory rectangular bhattacharyya's coordinates role of multiplication and inversion |
| title | A NOVEL CONCEPT: THE PRODUCT OF TWO NEGATIVELY DIRECTED NUMBERS IS A NEGATIVELY DIRECTED NUMBER THOUGH THE NEGATIVE OF A NEGATIVE NUMBER IS A POSITIVE NUMBER |
| title_full | A NOVEL CONCEPT: THE PRODUCT OF TWO NEGATIVELY DIRECTED NUMBERS IS A NEGATIVELY DIRECTED NUMBER THOUGH THE NEGATIVE OF A NEGATIVE NUMBER IS A POSITIVE NUMBER |
| title_fullStr | A NOVEL CONCEPT: THE PRODUCT OF TWO NEGATIVELY DIRECTED NUMBERS IS A NEGATIVELY DIRECTED NUMBER THOUGH THE NEGATIVE OF A NEGATIVE NUMBER IS A POSITIVE NUMBER |
| title_full_unstemmed | A NOVEL CONCEPT: THE PRODUCT OF TWO NEGATIVELY DIRECTED NUMBERS IS A NEGATIVELY DIRECTED NUMBER THOUGH THE NEGATIVE OF A NEGATIVE NUMBER IS A POSITIVE NUMBER |
| title_short | A NOVEL CONCEPT: THE PRODUCT OF TWO NEGATIVELY DIRECTED NUMBERS IS A NEGATIVELY DIRECTED NUMBER THOUGH THE NEGATIVE OF A NEGATIVE NUMBER IS A POSITIVE NUMBER |
| title_sort | novel concept the product of two negatively directed numbers is a negatively directed number though the negative of a negative number is a positive number |
| topic | bhattacharyya's theorem concept of limit number theory rectangular bhattacharyya's coordinates role of multiplication and inversion |
| url | https://jmcms.s3.amazonaws.com/wp-content/uploads/2024/10/10060129/jmcms-2409031-Negatively-Directed-Numbers-PCB.pdf |
| work_keys_str_mv | AT prabirchandrabhattacharyya anovelconcepttheproductoftwonegativelydirectednumbersisanegativelydirectednumberthoughthenegativeofanegativenumberisapositivenumber AT prabirchandrabhattacharyya novelconcepttheproductoftwonegativelydirectednumbersisanegativelydirectednumberthoughthenegativeofanegativenumberisapositivenumber |