Volume 7, Issue 3, June 2018, Page: 20-36
Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution
Wangui Patrick Mwangi, Department of Mathematics and Computer Science, University of Eldoret, Eldoret, Kenya
Received: Apr. 17, 2018;       Accepted: May 14, 2018;       Published: Aug. 8, 2018
DOI: 10.11648/j.pamj.20180703.11      View  596      Downloads  92
Abstract
The division by zero has been a challenge over years, which is in two forms: one involves a non-zero numerator while the other involves a zero numerator. This work deals with the second form of division, with the aim of finding a solution to the equation obtained when the expression is equated to, say x, where x is not a quantity but the ‘number of times of one whole’. In this work, zero divided by itself has been exhausted using different approaches and methods to come to a conclusion; that this division has a unique solution, 1. Some of the methods employed include geometric series, logarithm, indices, reciprocals, factorials, self-operations, Euler’s number, binomial expansions, graphical method among others. The conclusion has been made that zero divided by zero is 1. The reverse of division by multiplication is not applicable because zero has been associated with two ‘abnormal’ properties or behaviour that’s not with other numbers.
Keywords
Times of One Whole, Self-Operations, Shifting Method
To cite this article
Wangui Patrick Mwangi, Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution, Pure and Applied Mathematics Journal. Vol. 7, No. 3, 2018, pp. 20-36. doi: 10.11648/j.pamj.20180703.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Dodge, C. W. (1996). Division by zero. The Journal of the Mathematics Teacher, 89(2), 148. Retrieved March 6, 2018, from the JSTOR database.
[2]
Cajori, F. (1929). Absurdities due to division by zero, an historical note. The Journal of the Mathematics Teacher, 22(6), 336- 368. Retrieved March 6, 2018, from the JSTOR database.
[3]
Boyer, C. B. (1943). An early reference to division by zero. The Journal of the American Mathematical Monthly, 50(8), 487- 491. Retrieved March 6, 2018, from the JSTOR database.
[4]
Duncan, H. F. (1971). Division by zero. The Journal of the Arithmetic Teacher, 18(6), 381- 382. Retrieved March 6, 2018, from the JSTOR database.
[5]
Hornsby Jr., E. J. & Cole, C. (1985). Division by zero. The Journal of the Mathematics Teacher, 78(8), 588- 589. Retrieved March 6, 2018, from the JSTOR database.
[6]
Henry, B. (1969). Zero, the troublemaker. The Journal of the Arithmetic Teacher, 16(5), 365- 367. Retrieved March 6, 2018, from the JSTOR database.
[7]
Sunder, V. K. (1990). Thou shalt not divide by zero. The Journal of the Arithmetic Teacher, 37(7), 50- 51. Retrieved March 6, 2018, from the JSTOR database.
[8]
Lichtenberg, B. P. (1972). Zero is an even number. The Journal of the Arithmetic Teacher, 19(7), 535-538. Retrieved March 12, 2018, from the JSTOR database.
[9]
Allinger, G. D. (1980). Johnny got a zero today. The Journal of the Mathematics Teacher, 73(3), 187-190. Retrieved March 12, 2018, from the JSTOR database.
[10]
Ball L. D. (1990). Prospective Elementary and Secondary Teachers' Understanding of Division. Journal for Research in Mathematics Education, 21 (2), 132-144. Retrieved April 20, 2018, from the JSTOR database.
[11]
Carnahan, H. W. (1926). Note on the Fallacy. The Mathematics Teacher, 19(8), 496-498. Retrieved April 20, 2018, from the JSTOR database.
[12]
Sadi, A. (2007). Misconceptions in Numbers. UGRU Journal. 5(Fall 2007).
[13]
Heid, M. K. & et al (2013). Sampler: Division Involving Zero.
[14]
Matsuura, T. & Saitoh, S. (2016). Matrices and Division by Zero z/0 = 0. http://www.scirp.org/journal/alamt.
[15]
Jan, P. B. & Ilija, B. (2016). Anti Aristotle- The Division of Zero by Zero. Journal of Applied Mathematics and Physics. http://www.scirp.org/journal/jamp.
Browse journals by subject