Volume 3, Issue 4, August 2013, Pages 1015–1024
Manaye Getu Tsige1
1 Department of Agricultural Engineering, School of Engineering, Adama science and Technology University, Adama, Ethiopia
Original language: English
Copyright © 2013 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper presents the way to form other set of natural numbers from a given set of natural numbers and formulae to determine the sum of resulting numbers. The other set of natural numbers can be formed either by arranging a given natural numbers in specific order that is by using the principles of permutation rule or by using the principle of product rule provided that a given set of natural numbers should contain equal number of digits. The major areas of study to carry out this particular research work are probability rule, counting principles like permutation rule and product rule, and geometric series. Paper contains some essential theorems that help to arrive at main findings. The objective of this paper is to contribute additional knowledge to the Mathematical and Statistical science. The research results are two fundamental theorems and their applications in Mathematics, Statistics and other expected field of study. They are used to analyze complex numerical data computation and to create a password for a given numerical data with its importance to protect information flow management within a socio economic organization. The findings are foot step for the other related findings and applications that will be presented in the future. The future expected formulas or equations help to solve some difficult scientific and socio economic problems and also to derive approximation formula.
Author Keywords: Natural numbers, Probability rule, Product rule, Permutation rule, Geometric series.
Manaye Getu Tsige1
1 Department of Agricultural Engineering, School of Engineering, Adama science and Technology University, Adama, Ethiopia
Original language: English
Copyright © 2013 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper presents the way to form other set of natural numbers from a given set of natural numbers and formulae to determine the sum of resulting numbers. The other set of natural numbers can be formed either by arranging a given natural numbers in specific order that is by using the principles of permutation rule or by using the principle of product rule provided that a given set of natural numbers should contain equal number of digits. The major areas of study to carry out this particular research work are probability rule, counting principles like permutation rule and product rule, and geometric series. Paper contains some essential theorems that help to arrive at main findings. The objective of this paper is to contribute additional knowledge to the Mathematical and Statistical science. The research results are two fundamental theorems and their applications in Mathematics, Statistics and other expected field of study. They are used to analyze complex numerical data computation and to create a password for a given numerical data with its importance to protect information flow management within a socio economic organization. The findings are foot step for the other related findings and applications that will be presented in the future. The future expected formulas or equations help to solve some difficult scientific and socio economic problems and also to derive approximation formula.
Author Keywords: Natural numbers, Probability rule, Product rule, Permutation rule, Geometric series.
How to Cite this Article
Manaye Getu Tsige, “Theorems of Forming and Summing of Natural Numbers and Their Application,” International Journal of Innovation and Applied Studies, vol. 3, no. 4, pp. 1015–1024, August 2013.
