Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution

Wangui Patrick Mwangi

doi:doi:10.11648/j.pamj.20180703.11

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Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution

Wangui Patrick Mwangi

Published in Pure and Applied Mathematics Journal (Volume 7, Issue 3)

Received: 17 April 2018 Accepted: 14 May 2018 Published: 8 August 2018

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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.

Published in	Pure and Applied Mathematics Journal (Volume 7, Issue 3)
DOI	10.11648/j.pamj.20180703.11
Page(s)	20-36
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Times of One Whole, Self-Operations, Shifting Method

References

[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.

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Wangui Patrick Mwangi. (2018). Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution. Pure and Applied Mathematics Journal, 7(3), 20-36. https://doi.org/10.11648/j.pamj.20180703.11

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ACS Style

Wangui Patrick Mwangi. Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution. Pure Appl. Math. J. 2018, 7(3), 20-36. doi: 10.11648/j.pamj.20180703.11

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AMA Style

Wangui Patrick Mwangi. Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution. Pure Appl Math J. 2018;7(3):20-36. doi: 10.11648/j.pamj.20180703.11

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@article{10.11648/j.pamj.20180703.11,
  author = {Wangui Patrick Mwangi},
  title = {Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution},
  journal = {Pure and Applied Mathematics Journal},
  volume = {7},
  number = {3},
  pages = {20-36},
  doi = {10.11648/j.pamj.20180703.11},
  url = {https://doi.org/10.11648/j.pamj.20180703.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20180703.11},
  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.},
 year = {2018}
}

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TY  - JOUR
T1  - Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution
AU  - Wangui Patrick Mwangi
Y1  - 2018/08/08
PY  - 2018
N1  - https://doi.org/10.11648/j.pamj.20180703.11
DO  - 10.11648/j.pamj.20180703.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
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AB  - 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.
VL  - 7
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ER  -

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Author Information

Wangui Patrick Mwangi

Department of Mathematics and Computer Science, University of Eldoret, Eldoret, Kenya

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APA Style

Wangui Patrick Mwangi. (2018). Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution. Pure and Applied Mathematics Journal, 7(3), 20-36. https://doi.org/10.11648/j.pamj.20180703.11

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ACS Style

Wangui Patrick Mwangi. Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution. Pure Appl. Math. J. 2018, 7(3), 20-36. doi: 10.11648/j.pamj.20180703.11

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AMA Style

Wangui Patrick Mwangi. Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution. Pure Appl Math J. 2018;7(3):20-36. doi: 10.11648/j.pamj.20180703.11

Copy | Download

@article{10.11648/j.pamj.20180703.11,
  author = {Wangui Patrick Mwangi},
  title = {Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution},
  journal = {Pure and Applied Mathematics Journal},
  volume = {7},
  number = {3},
  pages = {20-36},
  doi = {10.11648/j.pamj.20180703.11},
  url = {https://doi.org/10.11648/j.pamj.20180703.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20180703.11},
  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.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution
AU  - Wangui Patrick Mwangi
Y1  - 2018/08/08
PY  - 2018
N1  - https://doi.org/10.11648/j.pamj.20180703.11
DO  - 10.11648/j.pamj.20180703.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 20
EP  - 36
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20180703.11
AB  - 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.
VL  - 7
IS  - 3
ER  -

Copy | Download