he spirit of three ‘C’
[ Dr. Hage Tabyo ]
First – ‘C’: To keep oneself ‘Cool’.
“Anyone can become angry – that is easy, but to be angry with the right person, to the right degree, at the right time, for the right purpose, and in the right way – that is not easy”, taught the renowned Greek philosopher, Aristotle.
With all the stress and pressure in our lives, it is easy to lose our cool at the slightest of irritations, or with the mildest of provocations. While we are rushing home from work at the end of another exhausting day, we scream at the slow paced moving driver on the road in front of us, who apparently has all the time in the world, not making our way, or while we shop at the grocery store, we get annoyed with the shopkeeper who makes delays in delivery of goods when we are in search of the ingredients for the night’s dinner menu. Or, while we are taking a tea break at the office canteen, we yell at the mobile retail vendor who has the nerve to interrupt us in an attempt to sell us his latest head load wares.
The problem with losing your temper on a daily basis is that it becomes a habit. And like most habits, a time arrives when it becomes second nature. Personal relationships start unraveling, business partnerships begin to fall apart and your credibility decreases as you become known as a ‘hot headed’ or ‘a loose cannon’. Effective people are consistent and in many ways, predictable. Tough times call for cool people and they are always cool and calm when pressure is on. Keeping your cool in a moment of crisis can save you years of pain and anguish. Hurtful words unleashed in a single minute of anger have led to many broken relationships. Words are like arrows, once released, they are impossible to retrieve. So one should choose one’s with care. Keeping cool could not only lower your blood pressure level and minimize probable heart attacks, but also increase the overall health of physical and social environment. “Treat people as if they were what they ought to be and help them become what they are capable of being” said the famous German poet, Johann Wolfgang Von Goethe. These are wise words to live by.
Second ‘C’: to ‘Connect’ with nature and plant trees.
We live in an age of seemingly limitless information. You may imagine: the weekday’s edition of the Hindustan Times newspaper contains more information than the average person was exposed to during an entire lifetime in the eighteenth century Indian life. Over these few years, I have experienced and found that spending time alone in natural surroundings in a forest connects me to the larger universe around me and restores my spirit in this hurried age.
After a busy week or a month of engagements in office or elsewhere with maddening associations with people, the simple act of sitting in a wooded park or forest-land and listening to the wind move through the leaves fills me with a sense of quiet and peace. My priorities become clearer, my obligations seem less pressing and my mind grows still. There is an absolute tone of peace of mind at the moment. Communing with nature is also an excellent way to unlock your creativity and generate new ideas as I sense. Isaac Newton formulated the Laws of Gravity while relaxing under an apple tree one day. Likewise, Swiss Designer George De Mestral developed Velcro after examining the burdock burrs that clung to his dog while he was hiking in the mountains. Natural surroundings serve to stifle the endless chatter that fills our minds so that our true brilliance can be liberated.
And while you spend time enjoying nature, observe your surroundings with deep concentration. Study the complexities of a flower or the way the wind current moves in a sparkling stream. Take your shoes off and feel the grass under your feet. Give silent thanks that you have the privilege of enjoying these special gifts of nature. Many people do not have that privilege, especially those who’re urbanites. As Mahatma Gandhi observed, “when I admire the wonder of a sunset or a beauty of the moon, my soul expands in worship of the Creator”.
According to ancient eastern thinking, to live a fulfilling life, you must do three things: have a son, write a book and plant a tree. By doing so, the thinking goes, you will have three legacies that will live on long after you die.
While there are clearly many more elements of a happy and complete life (I would add the joy of having a daughter too to the list), the idea of planting a tree is an excellent one. Watching a tree grow from a small sapling into a tall oak will keep you connected with the daily passage of time and the cycles of nature. Just as the tree grows and matures, so too will you be able to mark your personal passages and growth as a human being.
Third – ‘C’: ‘Carry a book with you, always.
I think, it is an ideal way of a habit which I for one use to make for a long time since, to keep and carry a good book in your kit wherever you go- always. It is one of the simplest yet useful ways of time management strategies you can follow to go anywhere with a book inside your travel bag. At any moment of stopgap eventuality, while others waiting in the line are complaining, you will be growing and feeding your mind with a rich diet of ideas found in great books – irrespective of whether may be that from novels, quotation books or history.
“So long as you live, keep learning how to live”, noted the Roman philosopher Seneca. Yet most people, especially among today’s youth never read more than a handful of books after they complete their formal schooling or college curricula. In these times of rapid change, ideas are the commodity of success in life. All it takes is one idea from the right book to reshape your character or transform your relationships or revolutionize your life. A good book can change the way you live as the philosopher – Henry David Thorean observed in ‘Walden’ – “There are probably words addressed to our condition exactly, which if we could really hear and understand, would be more salutary than the morning or the spring to our lives, and possibly put a new aspect on the face of things for us. How many a man has dated a new era of his life from reading a book. The book exists for us perchance which will explain our miracles and reveal new ones”.
How high you will rise in your life will be determined not by how hard you work or how much you amass wealth, but by how well you think. As Robin Sharma of ‘The monk who sold his Ferrari fame says in his leadership speeches. “The greatest leaders in this new economy will be the greatest thinkers”. And the person you will be five years from now will come down to two primary influences: books you read, and people you associate with.
Deep reading allows you to connect with the world’s most creative, intelligent and inspiring people, 24 hours a day. Aristotle, Emerson, Gandhi, Thoreau, Dorothea Brandi, and many more of the wisest of the men and women who graced our planet today are just waiting to share their knowledge with you through their books. Why would not you seize such an opportunity as often you could? If you have not read them today, you have not really lived today. And knowing how to read but failing to do so puts you in exactly the same position as the person who cannot read but wants to. (The writer is former Director of Health & Family Welfare, Govt of Arunachal Pradesh, Itanagar)
First – ‘C’: To keep oneself ‘Cool’.
“Anyone can become angry – that is easy, but to be angry with the right person, to the right degree, at the right time, for the right purpose, and in the right way – that is not easy”, taught the renowned Greek philosopher, Aristotle.
With all the stress and pressure in our lives, it is easy to lose our cool at the slightest of irritations, or with the mildest of provocations. While we are rushing home from work at the end of another exhausting day, we scream at the slow paced moving driver on the road in front of us, who apparently has all the time in the world, not making our way, or while we shop at the grocery store, we get annoyed with the shopkeeper who makes delays in delivery of goods when we are in search of the ingredients for the night’s dinner menu. Or, while we are taking a tea break at the office canteen, we yell at the mobile retail vendor who has the nerve to interrupt us in an attempt to sell us his latest head load wares.
The problem with losing your temper on a daily basis is that it becomes a habit. And like most habits, a time arrives when it becomes second nature. Personal relationships start unraveling, business partnerships begin to fall apart and your credibility decreases as you become known as a ‘hot headed’ or ‘a loose cannon’. Effective people are consistent and in many ways, predictable. Tough times call for cool people and they are always cool and calm when pressure is on. Keeping your cool in a moment of crisis can save you years of pain and anguish. Hurtful words unleashed in a single minute of anger have led to many broken relationships. Words are like arrows, once released, they are impossible to retrieve. So one should choose one’s with care. Keeping cool could not only lower your blood pressure level and minimize probable heart attacks, but also increase the overall health of physical and social environment. “Treat people as if they were what they ought to be and help them become what they are capable of being” said the famous German poet, Johann Wolfgang Von Goethe. These are wise words to live by.
Second ‘C’: to ‘Connect’ with nature and plant trees.
We live in an age of seemingly limitless information. You may imagine: the weekday’s edition of the Hindustan Times newspaper contains more information than the average person was exposed to during an entire lifetime in the eighteenth century Indian life. Over these few years, I have experienced and found that spending time alone in natural surroundings in a forest connects me to the larger universe around me and restores my spirit in this hurried age.
After a busy week or a month of engagements in office or elsewhere with maddening associations with people, the simple act of sitting in a wooded park or forest-land and listening to the wind move through the leaves fills me with a sense of quiet and peace. My priorities become clearer, my obligations seem less pressing and my mind grows still. There is an absolute tone of peace of mind at the moment. Communing with nature is also an excellent way to unlock your creativity and generate new ideas as I sense. Isaac Newton formulated the Laws of Gravity while relaxing under an apple tree one day. Likewise, Swiss Designer George De Mestral developed Velcro after examining the burdock burrs that clung to his dog while he was hiking in the mountains. Natural surroundings serve to stifle the endless chatter that fills our minds so that our true brilliance can be liberated.
And while you spend time enjoying nature, observe your surroundings with deep concentration. Study the complexities of a flower or the way the wind current moves in a sparkling stream. Take your shoes off and feel the grass under your feet. Give silent thanks that you have the privilege of enjoying these special gifts of nature. Many people do not have that privilege, especially those who’re urbanites. As Mahatma Gandhi observed, “when I admire the wonder of a sunset or a beauty of the moon, my soul expands in worship of the Creator”.
According to ancient eastern thinking, to live a fulfilling life, you must do three things: have a son, write a book and plant a tree. By doing so, the thinking goes, you will have three legacies that will live on long after you die.
While there are clearly many more elements of a happy and complete life (I would add the joy of having a daughter too to the list), the idea of planting a tree is an excellent one. Watching a tree grow from a small sapling into a tall oak will keep you connected with the daily passage of time and the cycles of nature. Just as the tree grows and matures, so too will you be able to mark your personal passages and growth as a human being.
Third – ‘C’: ‘Carry a book with you, always.
I think, it is an ideal way of a habit which I for one use to make for a long time since, to keep and carry a good book in your kit wherever you go- always. It is one of the simplest yet useful ways of time management strategies you can follow to go anywhere with a book inside your travel bag. At any moment of stopgap eventuality, while others waiting in the line are complaining, you will be growing and feeding your mind with a rich diet of ideas found in great books – irrespective of whether may be that from novels, quotation books or history.
“So long as you live, keep learning how to live”, noted the Roman philosopher Seneca. Yet most people, especially among today’s youth never read more than a handful of books after they complete their formal schooling or college curricula. In these times of rapid change, ideas are the commodity of success in life. All it takes is one idea from the right book to reshape your character or transform your relationships or revolutionize your life. A good book can change the way you live as the philosopher – Henry David Thorean observed in ‘Walden’ – “There are probably words addressed to our condition exactly, which if we could really hear and understand, would be more salutary than the morning or the spring to our lives, and possibly put a new aspect on the face of things for us. How many a man has dated a new era of his life from reading a book. The book exists for us perchance which will explain our miracles and reveal new ones”.
How high you will rise in your life will be determined not by how hard you work or how much you amass wealth, but by how well you think. As Robin Sharma of ‘The monk who sold his Ferrari fame says in his leadership speeches. “The greatest leaders in this new economy will be the greatest thinkers”. And the person you will be five years from now will come down to two primary influences: books you read, and people you associate with.
Deep reading allows you to connect with the world’s most creative, intelligent and inspiring people, 24 hours a day. Aristotle, Emerson, Gandhi, Thoreau, Dorothea Brandi, and many more of the wisest of the men and women who graced our planet today are just waiting to share their knowledge with you through their books. Why would not you seize such an opportunity as often you could? If you have not read them today, you have not really lived today. And knowing how to read but failing to do so puts you in exactly the same position as the person who cannot read but wants to. (The writer is former Director of Health & Family Welfare, Govt of Arunachal Pradesh, Itanagar)
読んでとても参考になりました：
\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,amssymb,amsfonts,amstext,amsthm}
\numberwithin{equation}{section}
\begin{document}
\title{\bf Announcement 281 : The importance of the division by zero $z/0=0$}
\author{ Institute of Reproducing Kernels\\
\date{February 1, 2016}
\maketitle
{\bf Abstract: } In this announcement, we will state the importance of the division by zero $z/0=0$. The result is a definite one and it is fundamental in mathematics.
\bigskip
{\bf Introduction}
\bigskip
%\label{sect1}
By {\bf a natural extension of the fractions}
\begin{equation}
\frac{b}{a}
\end{equation}
for any complex numbers $a$ and $b$, we found the result, for any complex number $b$
\begin{equation}
\frac{b}{0}=0,
\end{equation}
incidentally in \cite{s} by the Tikhonov regularization for the Hadamard product inversions for matrices, and we discussed their properties and gave several physical interpretations on the general fractions in \cite{kmsy} for the case of real numbers. The result is a very special case for general fractional functions in \cite{cs}.
The division by zero has a long and mysterious story over the world (see, for example, Google site with division by zero) with its physical viewpoints since the document of zero in India on AD 628, however,
Sin-Ei, Takahasi (\cite{kmsy}) established a simple and decisive interpretation (0.2) by analyzing some full extensions of fractions and by showing the complete characterization for the property (0.2). His result will show that our mathematics says that the result (0.2) should be accepted as a natural one:
\bigskip
{\bf Proposition. }{\it Let F be a function from ${\bf C }\times {\bf C }$ to ${\bf C }$ such that
$$
F (b, a)F (c, d)= F (bc, ad)
$$
for all
$$
a, b, c, d \in {\bf C }
$$
and
$$
F (b, a) = \frac {b}{a }, \quad a, b \in {\bf C }, a \ne 0.
$$
Then, we obtain, for any $b \in {\bf C } $
$$
F (b, 0) = 0.
$$}
\medskip
\medskip
We thus should consider, for any complex number $b$, as (0.2);
that is, for the mapping
\begin{equation}
w = \frac{1}{z},
\end{equation}
the image of $z=0$ is $w=0$. This fact seems to be a curious one in connection with our well-established popular image for the point at infinity on the Riemann sphere. Therefore, the division by zero will give great impacts to complex analysis and to our idea for the space and universe.
However, the division by zero (0.2) is now clear, indeed, for the introduction of (0.2), we have several independent approaches as in:
\medskip
1) by the generalization of the fractions by the Tikhonov regularization or by the Moore-Penrose generalized inverse,
\medskip
2) by the intuitive meaning of the fractions (division) by H. Michiwaki,
\medskip
3) by the unique extension of the fractions by S. Takahasi, as in the above,
\medskip
4) by the extension of the fundamental function $W = 1/z$ from ${\bf C} \setminus \{0\}$ into ${\bf C}$ such that $W =1/z$ is a one to one and onto mapping from $ {\bf C} \setminus \{0\} $ onto ${\bf C} \setminus \{0\}$ and the division by zero $1/0=0$ is a one to one and onto mapping extension of the function $W =1/z $ from ${\bf C}$ onto ${\bf C}$,
\medskip
and
\medskip
5) by considering the values of functions with the mean values of functions.
\medskip
Furthermore, in (\cite{msy}) we gave the results in order to show the reality of the division by zero in our world:
\medskip
\medskip
A) a field structure containing the division by zero --- the Yamada field ${\bf Y}$,
\medskip
B) by the gradient of the $y$ axis on the $(x,y)$ plane --- $\tan \frac{\pi}{2} =0$,
\medskip
C) by the reflection $1/\overline{z}$ of $z$ with respect to the unit circle with center at the origin on the complex $z$ plane --- the reflection point of zero is zero,
\medskip
and
\medskip
D) by considering rotation of a right circle cone having some very interesting
phenomenon from some practical and physical problem --- EM radius.
\medskip
See also \cite{bht} for the relationship between fields and the division by zero, and the importance of the division by zero for computer science.
\medskip
Meanwhile, Professors J. P. Barukcic and I. Barukcic (\cite{bb}) discussed recently the relation between the division $0/0$ and special relative theory of Einstein.
Furthermore, Reis and Anderson (\cite{ra,ra2}) extends the system of the real numbers by defining division by zero.
For our results, see the survey style announcements 179,185,237,246, 247,250 and 252 of the Institute of Reproducing Kernels (\cite{ann179,ann185,ann237,ann246,ann247,ann250,ann252}).
At this moment, the following theorem may be looked as the fundamental theorem of the division by zero:
\bigskip
{\bf Theorem (\cite{mst}).} {\it Any analytic function takes a definite value at an isolated singular point }{\bf with a natural meaning.}
\bigskip
The following corollary shows how to determine the value of an analytic function at the singular point; that is, the value is determined from the regular part of the Laurent expansion:
\bigskip
{\bf Corollary.} {\it For an isolated singular point $a$ of an analytic function $f(z)$, we have the Cauchy integral formula
$$
f(a) = \frac{1}{2\pi i} \int_{\gamma} f(z) \frac{dz}{z - a},
$$
where the $\gamma$ is a rectifiable simple Jordan closed curve that surrounds one time the point $a$
on a regular region of the function $f(z)$.
}
\bigskip
The essential meaning of this theorem and corollary is given by that: the values of functions may be understood in the sense of the mean values of analytic functions.
We will state the importance of the division by zero $z/0=0$.
\bigskip
\section{}
On AD 628, the zero was appeared in India in the document, and the zero division $z/0=0$ was discovered on Feburary 2, 2014, definitely with the clear definition and motievation. The uniquess and the natural interpretation were given in \cite{ttk,kmsy}, respectively. Several physical interpretations of the division by zero were given in \cite{kmsy}.
\bigskip
\section{}
By the introduction of the division by zero $z/0=0$, four arithmetic operations; that is,
addition, subtraction, multiplication, and division are always possible; note that for division, we were not able to divide by zero. There was one exceptional case for the division by zero.
Even the Yamada field containing the division by zero was established in (\cite{msy}).
\section{}
For the Euclidean (B.C. 3 Centuary ) geometry, two non-Euclidean geometries were appered about 2 hundred years ago, and in particular, in the elliptic type non-Euclidean geometry, the point at infinity was introduced by the stereoprojection of the Euclidean plane to the sphere and the concept is a standard one in complex analysis around over one hundered years. And then we have considered as $1/0= \infty$. However, surprisingly enough, the division by zero means that $1/0=0$.
\section{}
We will recall the fundamental law by Newton:
\begin{equation}
F = G\frac{m_1 m_2}{r^2}
\end{equation}
for two masses $m_1, m_2$ with a distance $r$ and a constant $G$. Of course,
\begin{equation}
\lim_{r \to +0} F =\infty,
\end{equation}
however, we obtain the important interpretation:
\begin{equation}
F = 0 = G \frac{m_1 m_2}{0}.
\end{equation}
Of course, here, we can consider the above interpretation for the mathematical formula (4.1) as the new interpretation (4.3). We can find many physical formulas with the division by zero.
See the following article for Einstein and Newton:
Impact of 'Division by Zero' in Einstein's Static Universe and ...\\
www.researchgate.net/.../242574738
Impact of 'Division by Zero' in Einstein's Static Universe and Newton's Equations in Classical Mechanics on ResearchGate, the professional network for.
In particular: George Gamow (1904-1968) Russian-born American nuclear physicist and cosmologist remarked that "it is well known to students of high school algebra" that division by zero is not valid; and Einstein admitted it as {\bf the biggest blunder of his life} [1]：
1. Gamow, G., My World Line (Viking, New York). p 44, 1970
\medskip
\section{}
In complex analysis, linear fractional functions
$$
W = \frac{az + b}{cz + d}, \quad ad -bc \ne 0,
$$
map the extended complex plane onto the extended complex plane containing the point at infinity, one to one, conformally, beautifully. This beautiful property is changed as the beautiful formula that linear fractional functions map the whole complex plane onto the whole complex plane, one to one, however, at one point of the singular point, the linear fractional functions have strong discontinuity.
The division by zero excludes the infinity from the numbers.
\section{}
We did, essentially, not consider the division by zero, and so the property of the division by zero; that is, at the isolated singular points of analytic functions, to consider the analytic functions are new mathematics and new research topics, essentially.
\section{}
The impact to complex analysis is unclear, we, however, obtain a typical new theorem:
\medskip
{\bf Theorem :} {\it Any analytic function takes a definite value at an isolated singular point }{\bf with a natural meaning.} The definite value is given by the first coefficient of the regular part in the Laurent expansion around the isolated singular point.
\medskip
This will be the fundamental theorem on the division by zero in Complex Analysis and we have many applications for the Sato hyperfunction theory, generating functions theory and singular integral theory (\cite{mst}).
\section{}
In particular, the divison by zero gives new interpretations on the finite part of Hadamard
for singular integrals and the Cauchy's principal values. The division by zero will represent discontinuity properties on the universe.
\section{}
Even for middle high shool students, the division by zero may be accepted as the beautiful result with great pleasures:
For the elementary function
$$
y = f(x) = \frac{1}{x},
$$
we have $f(0) = 0$; that is, $1/0=0$.
\section{}
We can introduce the division by zero $100/0=0,0/0=0$ with the simple and natural definition for the division by the Hiroshi Michiwachi method in the elementary school. The division by zero will request the change of all the related books and scientific books.
\section{Conclusion}
The division by zero $b/0=0$ is possible and the result is naturally determined, uniquely.
The result does not contradict with the present mathematics - however, in complex analysis, we need only to change a little presentation for the pole; not essentially, because we did not consider the division by zero, essentially.
The common understanding that the division by zero is impossible should be changed with many text books and mathematical science books. The definition of the fractions may be introduced by {\it the method of Michiwaki} in the elementary school, even.
Should we teach the beautiful fact, widely?:
For the elementary graph of the fundamental function
$$
y = f(x) = \frac{1}{x},
$$
$$
f(0) = 0.
$$
The result is applicable widely and will give a new understanding for the universe ({\bf Announcement 166}).
\medskip
If the division by zero $b/0=0$ is not introduced, then it seems that mathematics is incomplete in a sense, and by the intoduction of the division by zero, mathematics will become complete in a sense and perfectly beautiful.
\bigskip
\section{Remarks}
For the procedure of the developing of the division by zero and for some general ideas on the division by zero, we presented the following announcements in Japanese and English:
\medskip
{\bf Announcement 148} (2014.2.12): $100/0=0, 0/0=0$ -- by a natural extension of fractions -- A wish of the God
\medskip
{\bf Announcement 154} (2014.4.22): A new world: division by zero, a curious world, a new idea
\medskip
{\bf Announcement 157} (2014.5.8): We wish to know the idea of the God for the division by zero; why the infinity and zero point are coincident?
\medskip
{\bf Announcement 161} (2014.5.30): Learning from the division by zero, sprits of mathematics and of looking for the truth
\medskip
{\bf Announcement 163} (2014.6.17): The division by zero, an extremely pleasant mathematics - shall we look for the pleasant division by zero: a proposal for a fun club looking for the division by zero.
\medskip
{\bf Announcement 166} (2014.6.29): New general ideas for the universe from the viewpoint of the division by zero
\medskip
{\bf Announcement 171} (2014.7.30): The meanings of product and division -- The division by zero is trivial from the own sense of the division independently of the concept of product
\medskip
{\bf Announcement 176} (2014.8.9): Should be changed the education of the division by zero
\medskip
{\bf Announcement 179} (2014.10.22): Division by zero is clear as z/0=0 and it is fundamental in mathematics
\medskip
{\bf Announcement 185}: The importance of the division by zero $z/0=0$
\medskip
{\bf Announcement 237}（2015.6.18）: A reality of the division by zero $z/0=0$ by geometrical optics
\medskip
{\bf Announcement 246}: An interpretation of the division by zero $1/0=0$ by the gradients of lines
\medskip
{\bf Announcement 247}: The gradient of y-axis is zero and $\tan (\pi/2) =0$ by the division by zero $1/0=0$
\medskip
{\bf Announcement 250}(2015.10.20): What are numbers? - the Yamada field containing the division by zero $z/0=0$
\medskip
{\bf Announcement 252}: Circles and curvature - an interpretation by Mr. Hiroshi Michiwaki of the division by zero $r/0=0$
\medskip
{\bf Announcement 258}(2015.11.26): A new viewpoint of the division by zero $z/0=0$ from area and the point at infinity
\medskip
{\bf Announcement 275}(2016.1.11): The division by zero $z/0=0$ and special relative theory of Einstein
\medskip
\bigskip
\bibliographystyle{plain}
\begin{thebibliography}{10}
\bibitem{bb}
J. P. Barukcic and I. Barukcic, Anti Aristotle - The Division Of Zero By Zero,
ViXra.org (Friday, June 5, 2015)
© Ilija Barukčić, Jever, Germany. All rights reserved. Friday, June 5, 2015 20:44:59.
\bibitem{bht}
J. A. Bergstra, Y. Hirshfeld and J. V. Tucker,
Meadows and the equational specification of division (arXiv:0901.0823v1[math.RA] 7 Jan 2009).
\bibitem{cs}
L. P. Castro and S. Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.
\bibitem{kmsy}
M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane,
New meanings of the division by zero and interpretations on $100/0=0$ and on $0/0=0$,
Int. J. Appl. Math. {\bf 27} (2014), no 2, pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
\bibitem{msy}
H. Michiwaki, S. Saitoh, and M.Yamada,
Reality of the division by zero $z/0=0$. IJAPM (International J. of Applied Physics and Math. 6(2015), 1--8. http://www.ijapm.org/show-63-504-1.html
\bibitem{mst}
H. Michiwaki, S. Saitoh and M. Takagi,
A new concept for the point at infinity and the division by zero z/0=0
(manuscript).
\bibitem{ra}
T. S. Reis and James A.D.W. Anderson,
Transdifferential and Transintegral Calculus,
Proceedings of the World Congress on Engineering and Computer Science 2014 Vol I
WCECS 2014, 22-24 October, 2014, San Francisco, USA
\bibitem{ra2}
T. S. Reis and James A.D.W. Anderson,
Transreal Calculus,
IAENG International J. oF Applied Math., 45: %IJAM_45_1_06.
\bibitem{s}
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. {\bf 4} (2014), no. 2, 87--95. http://www.scirp.org/journal/ALAMT/
\bibitem{ttk}
S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operations on the real and complex fields, Tokyo Journal of Mathematics, {\bf 38}(2015), no. 2, 369-380.
\bibitem{ann179}
Announcement 179 (2014.8.30): Division by zero is clear as z/0=0 and it is fundamental in mathematics.
\bibitem{ann185}
Announcement 185 (2014.10.22): The importance of the division by zero $z/0=0$.
\bibitem{ann237}
Announcement 237 (2015.6.18): A reality of the division by zero $z/0=0$ by geometrical optics.
\bibitem{ann246}
Announcement 246 (2015.9.17): An interpretation of the division by zero $1/0=0$ by the gradients of lines.
\bibitem{ann247}
Announcement 247 (2015.9.22): The gradient of y-axis is zero and $\tan (\pi/2) =0$ by the division by zero $1/0=0$.
\bibitem{ann250}
Announcement 250 (2015.10.20): What are numbers? - the Yamada field containing the division by zero $z/0=0$.
\bibitem{ann252}
Announcement 252 (2015.11.1): Circles and
curvature - an interpretation by Mr.
Hiroshi Michiwaki of the division by
zero $r/0 = 0$.
\bibitem{ann258}
Announcement 258(2015.11.26): A new viewpoint of the division by zero $z/0=0$ from area and the point at infinity.
\bibitem{ann275}
Announcement 275(2016.1.11): The division by zero $z/0=0$ and special relative theory of Einstein.
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