0除算に関するアナウンスメントを公開していますThe purpose of this site is to publish announcements on the theory of division by zero
http://okmr.yamatoblog.net/
jaCopyright (C) 2005-2008 SAMURAI-FACTORY ALL RIGHTS RESERVED.Moore Penrose generalized inverse<img src="http://file.okmr.yamatoblog.net/2018040280782.jpg" alt="" />
http://okmr.yamatoblog.net/division%20by%20zero/moore%20penrose%20generalized
A naturality of $1/0=0$<img src="http://file.okmr.yamatoblog.net/2018040130768.jpg" alt="" />
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Announcement 409: Various Publication Projects on the Division by Zero <div style="text-align: center;">Institute of Reproducing Kernels</div><div style="text-align: center;">Kawauchi-cho, 5-1648-16,</div><div style="text-align: center;">Kiryu 376-0041, Japan</div>January 29, 2018<br />
<br />
The Institute of Reproducing Kernels is dealing with the theory of division<br />
by zero calculus and declares that the division by zero was discovered as 0/0 =<br />
1/0 = z/0 = 0 in a natural sense on 2014.2.2. The result shows a new basic<br />
idea on the universe and space since Aristoteles $($BC384 - BC322$)$ and Euclid<br />
$($BC 3 Century - $)$, and the division by zero is since Brahmagupta $($598 - 668<br />
?$)$. In particular, Brahmagupta defined as 0/0 = 0 in Brhmasphuasiddhnta<br />
$($628$)$, however, our world history stated that his definition 0/0 = 0 is wrong<br />
over 1300 years, but, we showed that his definition is suitable. For the details,<br />
see the references and the site: http://okmr.yamatoblog.net/<br />
We wrote two global book manuscripts [16] with 154 pages and [17] with<br />
many figures for some general people. Their main points are:<br />
<br />
• The division by zero and division by zero calculus are new elementary<br />
and fundamental mathematics in the undergraduate level.<br />
• They introduce a new space since Aristoteles $($BC384 - BC322$)$ and<br />
Euclid $($BC 3 Century - $)$ with many exciting new phenomena and<br />
properties with general interest, not specialized and difficult topics.<br />
However, their properties are mysterious and very attractive.<br />
• The contents are very elementary, however very exciting with general<br />
interest.<br />
• The contents give great impacts to our basic ideas on the universe and<br />
human beings.<br />
<br />
Meanwhile, the representations of the contents are very important and<br />
delicate with delicate feelings to the division by zero with a long and myste-<br />
rious history. Therefore, we hope the representations of the division by zero<br />
as follows:<br />
<br />
• Various book publications by many native languages and with the au-<br />
thor’s idea and feelings.<br />
• Some publications are like arts and some comic style books with pic-<br />
tures.<br />
• Some T shirts design, some pictures, monument design may be consid-<br />
ered.<br />
<br />
The authors above may be expected to contribute to our culture, educa-<br />
tion, common communications and enjoyments.<br />
For the people having the interest on the above projects, we will send our<br />
book sources with many figure files.<br />
How will be our project introducing our new world since Euclid?<br />
Of course, as mathematicians we have to publish new books on<br />
Calculus, Differential Equations and Complex Analysis, at least and soon,<br />
in order to correct them in some complete and beautiful ways.<br />
Our topics will be interested in over 1000 millions people over the world<br />
on the world history.<br />
<br />
<strong>References</strong><br />
[1] M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane, New mean-<br />
ings of the division by zero and interpretations on 100/0 = 0 and<br />
on 0/0 = 0, Int. J. Appl. Math. 27(2) $($2014$)$ 191-198, DOI:<br />
10.12732/ijam.v27i2.9.<br />
[2] T. Matsuura and S. Saitoh, Matrices and division by zero z/0 = 0,<br />
Advances in Linear Algebra & Matrix Theory, 6$($2016$)$, 51-58 Published<br />
Online June 2016 in SciRes. http://www.scirp.org/journal/alamt<br />
http://dx.doi.org/10.4236/alamt.2016.62007.<br />
[3] T. Matsuura and S. Saitoh, Division by zero calculus and singular inte-<br />
grals $($Submitted for publication$)$.<br />
[4] T. Matsuura, H. Michiwaki and S. Saitoh, $\log0=\log\infty=0$ and<br />
applications. Differential and Difference Equations with Applications.<br />
Springer Proceedings in Mathematics & Statistics.<br />
[5] H. Michiwaki, S. Saitoh and M.Yamada, Reality of the division by zero<br />
z/0 = 0. IJAPM International J. of Applied Physics and Math. 6 $($2015$)$,<br />
1–8. http://www.ijapm.org/show-63-504-1.html<br />
[6] H. Michiwaki, H. Okumura and S. Saitoh, Division by Zero z/0 = 0 in<br />
Euclidean Spaces, International Journal of Mathematics and Computa<br />
tion, 28$($2$)$$($2017$)$ 1-16.<br />
[7] H. Okumura, S. Saitoh and T. Matsuura, Relations of 0 and ∞, Journal<br />
of Technology and Social Science $($JTSS$)$, 1$($2017$)$ 70-77.<br />
[8] H. Okumura and S. Saitoh, The Descartes circles theorem and division<br />
by zero calculus. https://arxiv.org/abs/1711.04961 $($2017.11.14$)$.<br />
[9] H. Okumura, Wasan geometry with the division by 0.<br />
https://arxiv.org/abs/1711.06947 International Journal of Geometry.<br />
[10] H. Okumura and S. Saitoh, Applications of the division by zero calculus<br />
to Wasan geometry. $($Submitted for publication$)$.<br />
[11] S. Pinelas and S. Saitoh, Division by zero calculus and differential equa-<br />
tions. Differential and Difference Equations with Applications. Springer<br />
Proceedings in Mathematics & Statistics.<br />
[12] H. G. Romig, Discussions: Early History of Division by Zero, American<br />
Mathematical Monthly, Vol. 31, No. 8. $($Oct., 1924$)$, pp. 387-389.<br />
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<br />
http://okmr.yamatoblog.net/division%20by%20zero/announcement%20409-%20various
The division by zero: a comprehensive book We are planning on publishing a book with plenty of figures on the division by zero. The aim of the publication is to offer comprehensible examples using the definition of the division by zero. Before the publication, we would like to look for honest feedback widely from all over the world. <br />
<br />
Here is the link of the draft to download. <a href="http://file.okmr.yamatoblog.net/figure180308.pdf" target="_blank"> <br />
</a><a href="http://file.okmr.yamatoblog.net/figure180308.pdf" target="_blank"><br />
DOWNLOAD<br />
<br />
</a>Please send your comment to the address below. Any comments will welcome.<br />
<a href="hokmr@protonmail.com" title=""><span class="contact message-contact">hokmr@protonmail.com</span></a><a href="http://file.okmr.yamatoblog.net/figure180308.pdf" target="_blank"><br />
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</a><a href="http://file.okmr.yamatoblog.net/figure180308.pdf" target="_blank"><br />
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</a>
http://okmr.yamatoblog.net/division%20by%20zero/a%20comprehensible%20book%20on%20t
第１回 ゼロ除算研究集会のご案内下記のように研究集会を開催しますので、 ご案内致します。<div style="text-align: center;"><strong>第１回 ゼロ除算研究集会<br />
<br />
</strong></div><div style="text-align: center;"><strong>日時</strong>： ２０１８．３．１５（木曜日）．１１：００－１５：００</div><div style="text-align: center;"><strong>場所</strong>： 群馬大学大学院 理工学府<br />
<br />
</div><strong>概要</strong>： 始めにゼロ除算の全体について、齋藤三郎群馬大学名誉教授から３０分くら<br />
い 総合的な報告を受けて、その後、討論を重視する形で進める。昼食を挟んで、討<br />
論し、最後に 今後の研究活動について検討する。<br />
<br />
参加希望者は、下記にメールにて、お知らせ下さい：<br />
（kbdmm360@yahoo.co.jp , saburou.saitoh@gmail.com ）<br />
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http://okmr.yamatoblog.net/%E3%80%80/%E7%AC%AC%EF%BC%91%E5%9B%9E%E3%80%80%E3%82%BC%E3%83%AD%E9%99%A4%E7%AE%97%E7%A0%94%E7%A9%B6%E9%9B%86%E4%BC%9A%E3%81%AE%E3%81%94%E6%A1%88%E5%86%85
Announcement 412: The 4th birthday of the division by zero $z/0 = 0$<div style="text-align: center;">Institute of Reproducing Kernels</div><div style="text-align: center;">Kawauchi-cho, 5-1648-16,</div><div style="text-align: center;">Kiryu 376-0041, Japan</div><div style="text-align: center;"></div>February 2, 2018<br />
<br />
The Institute of Reproducing Kernels is dealing with the theory of division by zero calculus and declares that the division by zero was discovered as $0/0 =1/0 = z/0 = 0$ in a natural sense on 2014.2.2. The result shows a new basic idea on the universe and space since Aristotels $($BC384 - BC322$)$ and Euclid $($BC 3 Century - $)$, and the division by zero is since Brahmagupta $($598 - 668?$)$. In particular, Brahmagupta defined as $0/0 = 0$ in Brhmasphuasiddhnta $($628$)$, however, our world history stated that his definition $0/0 = 0$ is wrong over 1300 years, but, we showed that his definition is suitable. For the details, see the references and the site: http://okmr.yamatoblog.net/ We wrote a global book manuscript [21] with 154 pages and stated in the preface and last section of the manuscript as follows:<br />
<br />
<strong>Preface</strong><br />
The division by zero has a long and mysterious story over the world $($see, for example, H. G. Romig [15] and Google site with the division by zero$)$ with its physical viewpoints since the document of zero in India on AD 628. In particular, note that Brahmagupta $($598 -668 ?$)$ established the four arithmetic operations by introducing 0 and at the same time he defined as $0/0 = 0$ in Brhmasphuasiddhnta. Our world history, however, stated that his definition $0/0 = 0$ is wrong over 1300 years, but, we will see that his definition is right and suitable. <br />
The division by zero $1/0 = 0/0 = z/0$ itself will be quite clear and trivial with several natural extensions of the fractions against the mysterously long history, as we can see from the concepts of the Moore-Penrose generalized inverses or the Tikhonov regularization method to the fundamental equation $az = b$, whose solution leads to the definition $z = b/a$.<br />
However, the result $($definition$)$ will show that for the elementary mapping<br />
$$<br />
W =\frac{1}{z} \tag{0.1}<br />
$$the image of $z = 0$ is $W = 0$ $($should be defined from the form$)$. 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 ([1]). As the representation of the point at infinity of the Riemann sphere by the zero $z = 0$, we will see some delicate relations between 0 and $\infty$ which show a strong discontinuity at the point of infinity on the Riemann sphere. We did not consider any value of the elementary function $W = 1/z$ at the origin $z = 0$, because we did not consider the division by zero $1/0$ in a good way. Many and many people consider its value by the limiting like $+\infty$ and $-\infty$ or the point at infinity as $\infty$. However, their basic idea comes from continuity with the common sense or based on the basic idea of Aristotle. – For the related Greece philosophy, see [23, 24, 25]. However, as the division by zero we will consider its value of the function $W = 1/z$ as zero at $z = 0$. We will see that this new definition is valid widely in mathematics and mathematical sciences, see $($[9, 10]$)$ for example. Therefore, the division by zero will give great impacts to calculus, Euclidean geometry, analytic geometry, differential equations, complex analysis in the undergraduate level and to our basic ideas for the space and universe.<br />
We have to arrange globally our modern mathematics in our undergraduate level. Our common sense on the division by zero will be wrong, with our basic idea on the space and the universe since Aristotle and Euclid. We would like to show clearly these facts in this book. The content is in the undergraduate level.<br />
<br />
<strong>Conclusion</strong><br />
Apparently, the common sense on the division by zero with a long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on derivatives we have a great missing since $tan(\pi/2) = 0$. Our mathematics is also wrong in elementary mathematics on the division by zero. <br />
This book is an elementary mathematics on our division by zero as the first publication of books for the topics. The contents have wide connections to various fields beyond mathematics. The author expects the readers write some philosophy, papers and essays on the division by zero from this simple source book.<br />
The division by zero theory may be developed and expanded greatly as in the author’s conjecture whose break theory was recently given surprisingly and deeply by Professor Qi’an Guan [3] since 30 years proposed in [17] $($the original is in [16]$)$.<br />
We have to arrange globally our modern mathematics with our division by zero in our undergraduate level.<br />
We have to change our basic ideas for our space and world.<br />
We have to change globally our textbooks and scientific books on the division by zero.<br />
<br />
<strong>References</strong><br />
[1] L. V. Ahlfors, Complex Analysis, McGraw-Hill Book Company, 1966.<br />
[2] L. P. Castro and S. Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory 7 $($2013$)$, no. 4, 1049-1063.<br />
[3] Q. Guan, A proof of Saitoh’s conjecture for conjugate Hardy H2 kernels, arXiv:1712.04207.<br />
[4] 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. 27 $($2014$)$, no 2, pp. 191-198, DOI: 10.12732/ijam.v27i2.9.<br />
[5] T. Matsuura and S. Saitoh, Matrices and division by zero $z/0=0$, Advances in Linear Algebra & Matrix Theory, 6$($2016$)$, 51-58 Published Online June 2016 in SciRes. http://www.scirp.org/journal/alamt http://dx.doi.org/10.4236/alamt.2016.62007.<br />
[6] T. Matsuura and S. Saitoh, Division by zero calculus and singular integrals. $($Submitted for publication$)$<br />
[7] T. Matsuura, H. Michiwaki and S. Saitoh, log0 = log∞ = 0 and applications. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics.<br />
[8] 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<br />
[9] H. Michiwaki, H. Okumura and S. Saitoh, Division by Zero $z/0 = 0$ in Euclidean Spaces, International Journal of Mathematics and Computation, 28$($2017$)$; Issue 1, 1-16.<br />
[10] H. Okumura, S. Saitoh and T. Matsuura, Relations of 0 and ∞, Journal<br />
of Technology and Social Science $($JTSS$)$, 1$($2017$)$, 70-77.<br />
[11] H. Okumura and S. Saitoh, The Descartes circles theorem and division by zero calculus. https://arxiv.org/abs/1711.04961 $($2017.11.14$)$.<br />
[12] H. Okumura, Wasan geometry with the division by 0. https://arxiv.org/abs/1711.06947 International Journal of Geometry.<br />
[13] H. Okumura and S. Saitoh, Applications of the division by zero calculus to Wasan geometry. $($Submitted for publication$)$.<br />
[14] S. Pinelas and S. Saitoh, Division by zero calculus and differential equations. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics.<br />
[15] H. G. Romig, Discussions: Early History of Division by Zero, American<br />
Mathematical Monthly, Vol. 31, No. 8. $($Oct., 1924$)$, pp. 387-389.<br />
[16] S. Saitoh, The Bergman norm and the Szegö norm, Trans. Amer. Math. Soc. 249 $($1979$)$, no. 2, 261–279.<br />
[17] S. Saitoh, Theory of reproducing kernels and its applications. Pitman Research Notes in Mathematics Series, 189. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1988. x+157 pp. ISBN: 0-582-03564-3<br />
[18] S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra & Matrix Theory. 4 $($2014$)$, no. 2, 87–95. http://www.scirp.org/journal/ALAMT/<br />
[19] S. Saitoh, A reproducing kernel theory with some general applications, Qian,T./Rodino,L.$($eds.$)$: Mathematical Analysis, Probability and Applications - Plenary Lectures: Isaac 2015, Macau, China, Springer Proceedings in Mathematics and Statistics, 177(2016), 151-182. $($Springer$)$.<br />
[20] S. Saitoh, Mysterious Properties of the Point at Infinity、arXiv:1712.09467 [math.GM]$($2017.12.17$)$.<br />
[21] S. Saitoh, Division by zero calculus $($154 pages: draft$)$: $($http://okmr.yamatoblog.net/ $)$<br />
[22] S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operations on the real and complex fields, Tokyo Journal of Mathematics, 38$($2015$)$, no. 2, 369-380.<br />
[23] https://philosophy.kent.edu/OPA2/sites/default/files/012001.pdf<br />
[24] http://publish.uwo.ca/ jbell/The 20Continuous.pdf<br />
[25] http://www.mathpages.com/home/kmath526/kmath526.htm<br />
[26] Announcement 179 $($2014.8.30$)$: Division by zero is clear as z/0=0 and it is fundamental in mathematics.<br />
[27] Announcement 185 $($2014.10.22$)$: The importance of the division by zero $z/0 = 0$.<br />
[28] Announcement 237 $($2015.6.18$)$: A reality of the division by zero $z/0 = 0$ by geometrical optics.<br />
[29] Announcement 246 $($2015.9.17$)$: An interpretation of the division by zero $1/0 = 0$ by the gradients of lines.<br />
[30] 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$.<br />
[31] Announcement 250 $($2015.10.20$)$: What are numbers? - the Yamada field containing the division by zero z/0 = 0.<br />
[32] Announcement 252 $($2015.11.1$)$: Circles and curvature - an interpretation by Mr. Hiroshi Michiwaki of the division by zero $r/0 = 0$.<br />
[33] Announcement 281 $($2016.2.1$)$: The importance of the division by zero $z/0 = 0$.<br />
[34] Announcement 282 $($2016.2.2$)$: The Division by Zero z/0 = 0 on the Second Birthday.<br />
[35] Announcement 293 $($2016.3.27$)$: Parallel lines on the Euclidean plane from the viewpoint of division by zero $1/0=0$.<br />
[36] Announcement 300 $($2016.05.22$)$: New challenges on the division by zero $z/0=0$.<br />
[37] Announcement 326 $($2016.10.17$)$: The division by zero z/0=0 - its impact to human beings through education and research.<br />
[38] Announcement 352$($2017.2.2$)$: On the third birthday of the division by zero $z/0=0$.<br />
[39] Announcement 354$($2017.2.8)$:$ What are $n = 2,1,0$ regular polygons inscribed in a disc? – relations of 0 and infinity.<br />
[40] Announcement 362$($2017.5.5$)$: Discovery of the division by zero as $0/0 =<br />
1/0 = z/0 = 0$<br />
[41] Announcement 380 $($2017.8.21$)$: What is the zero?<br />
[42] Announcement 388$($2017.10.29$)$: Information and ideas on zero and division by zero $($a project$)$.<br />
[43] Announcement 409 $($2018.1.29.$)$: Various Publication Projects on the Division by Zero.<br />
[44] Announcement 410 $($2018.1 30.$)$: What is mathematics? – beyond logic; for great challengers on the division by zero.<br />
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http://okmr.yamatoblog.net/division%20by%20zero/announcement%20412-%20the%204th
Announcement 410: What is mathematics? -- beyond logic; for great challengers on the division by zero<div style="text-align: center;">Institute of Reproducing Kernels</div><div style="text-align: center;">Kawauchi-cho, 5-1648-16,</div><div style="text-align: center;">Kiryu 376-0041, Japan</div><div style="text-align: center;"></div>January 24, 2018<br />
<br />
The Institute of Reproducing Kernels is dealing with the theory of divisionby zero calculus and declares that the division by zero was discovered as $0/0 =1/0 = z/0 = 0$ in a natural sense on 2014.2.2. The result shows a new basic idea on the universe and space since Aristotels $($BC384 - BC322$)$ and Euclid $($BC 3 Century - $)$, and the division by zero is since Brahmagupta $($598 - 668?$)$. In particular, Brahmagupta defined as $0/0 = 0$ in Brhmasphuasiddhnta $($628$)$, however, our world history stated that his definition $0/0 = 0$ is wrong over 1300 years, but, we showed that his definition is suitable. For the details, see the references and the site: http://okmr.yamatoblog.net/ <br />
We wrote a global book manuscript [22] with 154 pages and stated that the division by zero is trivial and clear, and in the last section of the manuscript we stated as follows:<br />
<br />
<strong> Conclusion</strong><br />
Apparently, the common sense on the division by zero with a long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on derivatives we have a great missing since $\tan(π/2) = 0$. Our mathematics is also wrong in elementary mathematics on the division by zero.<br />
This book is an elementary mathematics on our division by zero as the first publication of books for the topics. The contents have wide connections to various fields beyond mathematics. The author expects the readers write some philosophy, papers and essays on the division by zero from this simple source book.<br />
The division by zero theory may be developed and expanded greatly as in the author’s conjecture whose break theory was recently given surprisingly and deeply by Professor Qi’an Guan [3] since 30 years proposed in [18] $($the original is in [17]$)$.<br />
We have to arrange globally our modern mathematics with our division by zero in our undergraduate level. <br />
We have to change our basic ideas for our space and world.<br />
We have to change globally our textbooks and scientific books on the division by zero.<br />
<br />
However, we have still curious situations and opinions for us on the division by zero; in particular, the two great challengers Jakub Czajko and Ilija Baruki on the division by zero in connection with physics stated that we do not have the definition of the division $0/0$, however $0/0 = 1$. They seem to think that a truth is based on physical objects and is not on our mathematics. In such a cases, we will not be able to continue discussions on the division by zero more, because for mathematicians, they will not be able to follow their logics more. However, then we will ask for the question that what are the values and contributions of your articles and discussions. We<br />
will expect some contributions, of course.<br />
This question will reflect to mathematicians contrary. We stated for the estimation of mathematisc in [16]: Mathematics is the collection of relations and, good results are fundamental, beautiful, and give great good impacts to human beings.<br />
With this estimation, we stated that the Euler formula<br />
$$e^{πi} = −1$$<br />
is the best result in mathematics in details in:<br />
No.81, May 2012$($pdf 432kb$)$ www.jams.or.jp/kaiho/kaiho-81.pdf<br />
In order to show the importance of our division by zero and division by zero calculus we are requested to show their importance.<br />
It seems that the long and mysterious confusions for the division by zero is on the definition. – Indeed, when we consider the division by zero $a/0$ in the usual sense of the fundamental equation 0 · $z = a$, we have immediately the simple contradiction, however, we have such cases may happen, in particular, in mathematical formulas and physical formulas on the universe.<br />
<br />
<strong>References</strong><br />
[1] I. Baruki, Dialectical Logic Negation Of Classical Logic, http://vixra.org/abs/1801.0256<br />
[2] J. Czajko, Algebraic division by zero implemented as quasigeometric multiplication by infinity in real and complex multispatial hyperspaces, Available online at www.worldscientificnews.com WSN 92$($2$)$ $($2018$)$ 171-197<br />
[3] Q. Guan, A proof of Saitoh’s conjecture for conjugate Hardy H2 kernels, arXiv:1712.04207.<br />
[4] 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. 27 $($2014$)$, no 2, pp. 191-198, DOI: 10.12732/ijam.v27i2.9.<br />
[5] T. Matsuura and S. Saitoh, Matrices and division by zero $z/0=0$, Advances in Linear Algebra & Matrix Theory, 6$($2016$)$, 51-58 Published Online June 2016 in SciRes. http://www.scirp.org/journal/alamt http://dx.doi.org/10.4236/alamt.2016.62007.<br />
[6] T. Matsuura and S. Saitoh, Division by zero calculus and singular integrals. $($Submitted for publication$)$<br />
[7] T. Matsuura, H. Michiwaki and S. Saitoh, $\log0 = \log\infty = 0$ and applications. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics.<br />
[8] 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<br />
[9] H. Michiwaki, H. Okumura and S. Saitoh, Division by Zero $z/0 = 0$ in Euclidean Spaces, International Journal of Mathematics and Computation, 28$($2017$)$; Issue 1 1-16.<br />
[10] H. Okumura, S. Saitoh and T. Matsuura, Relations of 0 and ∞, Journal of Technology and Social Science $($JTSS$)$, 1$($2017$)$, 70-77.<br />
[11] H. Okumura and S. Saitoh, The Descartes circles theorem and division by zero calculus. https://arxiv.org/abs/1711.04961 (2017.11.14).<br />
[12] H. Okumura, Wasan geometry with the division by 0. https://arxiv.org/abs/1711.06947 International Journal of Geometry.<br />
[13] H. Okumura and S. Saitoh, Applications of the division by zero calculus to Wasan geometry. $($Submitted for publication$)$.<br />
[14] S. Pinelas and S. Saitoh, Division by zero calculus and differential equations. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics.<br />
[15] H. G. Romig, Discussions: Early History of Division by Zero, American Mathematical Monthly, Vol. 31, No. 8. $($Oct., 1924$)$, pp. 387-389.<br />
[16] T. M. Rassias, Editor, Nonlinear Mathematical Analysis and Applications, HadronicPress,Palm Harbor,FL34682-1577,USA:ISBN1-57485-044-X,1998, pp.223234: Nonlinear transforms and analyticity of functions, Saburou Saitoh.<br />
[17] S. Saitoh, The Bergman norm and the Szegö norm, Trans. Amer. Math. Soc. 249 $($1979$)$, no. 2, 261–279.<br />
[18] S. Saitoh, Theory of reproducing kernels and its applications. Pitman Research Notes in Mathematics Series, 189. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1988. x+157 pp. ISBN: 0-582-03564-3<br />
[19] S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra & Matrix Theory. 4 $($2014$)$, no. 2, 87–95. http://www.scirp.org/journal/ALAMT/<br />
[20] S. Saitoh, A reproducing kernel theory with some general applications, Qian,T./Rodino,L.$($eds.$)$: Mathematical Analysis, Probability and Applications - Plenary Lectures: Isaac 2015, Macau, China, Springer Proceedings in Mathematics and Statistics, 177$($2016$)$, 151-182. $($Springer$)$<br />
.[21] S. Saitoh, Mysterious Properties of the Point at Infinity. arXiv:1712.09467 [math.GM]$($2017.12.17$)$.<br />
[22] S. Saitoh, Division by zero calculus $($154 pages: draft$)$: $($http://okmr.yamatoblog.net/ $)$<br />
[23] S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operations on the real and complex fields, Tokyo Journal of Mathematics, 38(2015), no. 2, 369-380.<br />
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http://okmr.yamatoblog.net/division%20by%20zero/announcement%20410-%20%20%20what%20i
Announcement 409: Various Publication Projects on the Division by Zero<div style="text-align: center;">Institute of Reproducing Kernels</div><div style="text-align: center;">Kawauchi-cho, 5-1648-16,</div><div style="text-align: center;">Kiryu 376-0041, Japan</div><div style="text-align: center;"></div>January 29, 2018<br />
<br />
The Institute of Reproducing Kernels is dealing with the theory of division by zero calculus and declares that the division by zero was discovered as 0/0 =1/0 = z/0 = 0 in a natural sense on 2014.2.2. The result shows a new basic idea on the universe and space since Aristoteles $($BC384 - BC322$)$ and Euclid $($BC 3 Century - $)$, and the division by zero is since Brahmagupta $($598 - 668?$)$. In particular, Brahmagupta defined as $0/0 = 0$ in Brhmasphuasiddhnta $($628$)$, however, our world history stated that his definition $0/0 = 0$ is wrong over 1300 years, but, we showed that his definition is suitable. For the details, see the references and the site: http://okmr.yamatoblog.net/<br />
We wrote two global book manuscripts [16] with 154 pages and [17] with many figures for some general people. Their main points are:<br />
<br />
• The division by zero and division by zero calculus are new elementary and fundamental mathematics in the undergraduate level.<br />
<br />
• They introduce a new space since Aristoteles $($BC384 - BC322$)$ and Euclid $($BC 3 Century - $)$ with many exciting new phenomena and properties with general interest, not specialized and difficult topics. However, their properties are mysterious and very attractive.<br />
<br />
Meanwhile, the representations of the contents are very important and delicate with delicate feelings to the division by zero with a long and mysterious history. Therefore, we hope the representations of the division by zero as follows:<br />
<br />
• Various book publications by many native languages and with the author’s idea and feelings.<br />
<br />
• Some publications are like arts and some comic style books with pictures.<br />
<br />
• Some T shirts design, some pictures, monument design may be consided. <br />
<br />
The authors above may be expected to contribute to our culture, education, common communications and enjoyments. For the people having the interest on the above projects, we will send our book sources with many figure files.<br />
How will be our project introducing our new world since Euclid?<br />
Of course, as mathematicians we have to publish new books on Calculus, Differential Equations and Complex Analysis, at least and soon, in order to <strong>correct them</strong> in some complete and beautiful ways.<br />
Our topics will be interested in over 1000 millions people over the world on the world history.<br />
<br />
<strong><strong><strong>References</strong></strong></strong><br />
[1] 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. 27 $($2014$)$, no 2, pp. 191-198, DOI:<br />
10.12732/ijam.v27i2.9.<br />
[2] T. Matsuura and S. Saitoh, Matrices and division by zero $z/0 = 0$, Advances in Linear Algebra & Matrix Theory, 6$($2016$)$, 51-58 Published Online June 2016 in SciRes. http://www.scirp.org/journal/alamt<br />
[3] T. Matsuura and S. Saitoh, Division by zero calculus and singular integrals. $($Submitted for publication$)$<br />
[4] T. Matsuura, H. Michiwaki and S. Saitoh, log0 = log∞ = 0 and applications. Differential and Difference Equations with Applications.Springer Proceedings in Mathematics & Statistics.<br />
[5] 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<br />
[6] H. Michiwaki, H. Okumura and S. Saitoh, Division by Zero z/0 = 0 in Euclidean Spaces, International Journal of Mathematics and Computation, 28$($1$)$$($2017$)$; 1-16.<br />
[7] H. Okumura, S. Saitoh and T. Matsuura, Relations of 0 and ∞, Journal of Technology and Social Science $($JTSS$)$, 1$($2017$)$, 70-77.<br />
[8] H. Okumura and S. Saitoh, The Descartes circles theorem and division by zero calculus. https://arxiv.org/abs/1711.04961 $($2017.11.14$)$.<br />
[9] H. Okumura, Wasan geometry with the division by 0. https://arxiv.org/abs/1711.06947 International Journal of Geometry.<br />
[10] H. Okumura and S. Saitoh, Applications of the division by zero calculus to Wasan geometry. $($Submitted for publication$)$.<br />
[11] S. Pinelas and S. Saitoh, Division by zero calculus and differential equations. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics.<br />
[12] H. G. Romig, Discussions: Early History of Division by Zero, American Mathematical Monthly, Vol. 31, No. 8.$($Oct., 1924$)$, pp. 387-389.<br />
[13] S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra & Matrix Theory. 4 $($2014$)$, no. 2, 87–95. http://www.scirp.org/journal/ALAMT/<br />
[14] S. Saitoh, A reproducing kernel theory with some general applications, Qian,T./Rodino,L.(eds.): Mathematical Analysis, Probability and Applications - Plenary Lectures: Isaac 2015, Macau, China, Springer Proceedings in Mathematics and Statistics, 177$($2016$)$, 151-182. $($Springer$)$.<br />
[15] S. Saitoh, Mysterious Properties of the Point at Infinity, arXiv:1712.09467 [math.GM]$($2017.12.17$)$.<br />
[16] S. Saitoh, Division by zero calculus $($154 pages: draft$)$: http//okmr.yamatoblog.net/<br />
[17] S. Saitoh and H. Okumura, Division by Zero Calculus in Figures – our New Space –<br />
[18] S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operations on the real and complex fields, Tokyo Journal of Mathematics, 38$($2015$)$, no. 2, 369-380.
http://okmr.yamatoblog.net/division%20by%20zero/announcement%20381-%20%20%20variou
An extensive draft on the division by zero An extensive 154 pages draft by Saburou Saitoh $($02/01/2018$)$ is available.<br />
<br />
The download link is below:<br />
<a href="http://file.okmr.yamatoblog.net/bso180102.pdf" title="" target="_self"><br />
</a><a href="http://file.okmr.yamatoblog.net/bso180102.pdf" title="" target="_self">Division by Zero Calculus</a><a href="http://file.okmr.yamatoblog.net/bso180102.pdf" target="_blank"><br />
</a><a href="http://file.okmr.yamatoblog.net/bso180102.pdf" target="_blank"><br />
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http://okmr.yamatoblog.net/division%20by%20zero/an%20extensive%20draft%20on%20the
Announcement 380: What is the zero?<div style="text-align: center;">Institute of Reproducing Kernels</div><div style="text-align: center;">Kawauchi-cho, 5-1648-16,</div><div style="text-align: center;">Kiryu 376-0041, Japan</div><div style="text-align: center;"></div>August 21, 2017<br />
<br />
<strong>1 What is the zero?<br />
<br />
</strong>The zero $0$ as the complex number or real number is given clearly by the axions by the complex number field and real number field.<br />
<br />
For this fundamental idea, we should consider the <strong>Yamada field </strong> containing the division by zero. The Yamada field and the division by zero calculus will arrange our mathematics, beautifully and completely; this will be our natural and complete mathematics. <br />
<br />
<br />
<strong>2 Double natures of the zero $z=0$ <br />
<br />
</strong>The zero point $z=0$ represents the double natures; one is the origin at the starting point and another one is a representation of the point at infinity. One typical and simple example is given by $e^0 = 1,0$, two values. <strong> God loves two.<br />
<br />
<br />
</strong><strong><strong>3 Standard value <br />
<br />
</strong></strong>The zero is a center and stand point $($or bases, a standard value$)$ of the coordinates - here we will consider our situation on the complex or real 2 dimensional spaces. By stereographic projection mapping or the Yamada field, the point at infinity $1/0$ is represented by zero. The origin of the coordinates and the point at infinity correspond each other.<strong><strong><br />
</strong></strong>  As the standard value, for the point $\omega_n = \exp \left(\frac{\pi}{n}i\right)$ on the unit circle $|z|=1$ on the complex $z$-plane is, for $n = 0$:<br />
\begin{equation}<br />
\omega_0 = \exp \left(\frac{\pi}{0}i\right)=1, \quad \frac{\pi}{0} =0.<br />
\end{equation}<br />
For the mean value <br />
$$<br />
M_n = \frac{x_1 + x_2 +... + x_n}{n},<br />
$$<br />
we have<br />
$$<br />
M_0 = 0 = \frac{0}{0}.<br />
$$<br />
<strong><strong><br />
4 Fruitful world<br />
<br />
</strong></strong>For example, for very and very general partial differential equations, if the coefficients or terms are zero, then we have some simple differential equations and the extreme case is all the terms are zero; that is, we have trivial equations $0=0$; then its solution is zero. When we consider the converse, we see that the zero world is a fruitful one and it means some vanishing world. Recall Yamane phenomena $($[1]$)$, the vanishing result is very simple zero, however, it is the result from some fruitful world. Sometimes, zero means void or nothing world, however, it will show <strong>some changes</strong> as in the Yamane phenomena.<strong><strong><br />
<br />
5 From $0$ to $0$; $0$ means all and all are $0$<br />
<br />
</strong></strong>As we see from our life figure $($[5]$)$, a story starts from the zero and ends with the zero. This will mean that $0$ means all and all are $0$. The zero is a <strong>mother</strong> or an <strong>origin</strong> of all.<strong><strong><br />
<br />
6 Impossibility<br />
<br />
</strong></strong>As the solution of the simplest equation<br />
\begin{equation}\tag{6.1}<br />
ax =b<br />
\end{equation}we have $x=0$ for $a=0, b\ne 0$ as the standard value, or the Moore-Penrose generalized inverse. This will mean in a sense, the solution does not exist; to solve the equation $($6.1$)$ is impossible. We saw for different parallel lines or different parallel planes, their common points are the origin. Certainly they have the common points of the point at infinity and the point at infinity is represented by zero. However, we can understand also that they have no solutions, no common points, because the point at infinity is an ideal point.<strong><strong><br />
</strong></strong>  Of course. we can consider the equation $($6.1$)$ even the case $a=b=0$ and then we have the solution $x=0$ as we stated.<strong><strong><br />
</strong></strong>  We will consider the simple differential equation<br />
\begin{equation}<br />
m\frac{d^2x}{dt^2} =0, m\frac{d^2y}{dt^2} =-mg<br />
\end{equation}<br />
with the initial conditions, at $t =0$<br />
\begin{equation}<br />
\frac{dx}{dt} = v_0 \cos \alpha , \frac{d^2x}{dt^2} = \frac{d^2y}{dt^2}=0.<br />
\end{equation}Then, the highest high $h$, arriving time $t$, the distance $d$ from the starting point at the origin to the point $y(2t) =0$ are given by<br />
\begin{equation}<br />
h = \frac{v_0 \sin^2 \alpha}{2g}, d= \frac{v_0\sin \alpha}{g}<br />
\end{equation}and<br />
\begin{equation}<br />
t= \frac{v_0 \sin \alpha}{g}.<br />
\end{equation}<br />
For the case $g=0$, we have $h=d =t=0$. We considered the case that they are the infinity; however, our mathematics means zero, which shows impossibility.<br />
  These phenomena were looked many cases on the universe; it seems that <strong>God does not like the infinity</strong>.<br />
<strong><strong><br />
</strong></strong><br />
<strong><strong><strong>References<br />
</strong></strong></strong>[1] 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. <strong>27</strong> $($2014$)$, no 2, pp. 191-198, DOI: 10.12732/ijam.v27i2.9.<strong><strong><strong><br />
</strong></strong></strong>[2] 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<strong><strong><strong><br />
</strong></strong></strong>[3] T. Matsuura and S. Saitoh, Matrices and division by zero $z/0=0$, Advances in Linear Algebra & Matrix Theory, <strong>6</strong> $($2016$)$, 51-58. http://dx.doi.org/10.4236/alamt.2016.62007 http://www.scirp.org/journal/alamt<strong><strong><strong><br />
</strong></strong></strong>[4] H. Michiwaki, H. Okumura, and S. Saitoh, Division by Zero $z/0 = 0$ in Euclidean Spaces. International Journal of Mathematics and Computation <strong>28</strong> $($2017$)$; Issue 1, 2017), 1-16.<strong><strong><strong><br />
</strong></strong></strong>[5] H. Okumura, S. Saitoh and T. Matsuura, Relations of $0$ and $\infty$, Journal of Technology and Social Science $($JTSS$)$, <strong>1</strong>$($2017$)$, 70-77.<strong><strong><strong><br />
</strong></strong></strong>[6] H. G. Romig, Discussions: Early History of Division by Zero, American Mathematical Monthly, Vol. 31, No. 8. $($Oct., 1924$)$, pp. 387-389.<strong><strong><strong><br />
</strong></strong></strong>[7] S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory.<strong><strong><strong> 4 </strong></strong></strong>$($2014$)$, no. 2, 87--95. http://www.scirp.org/journal/ALAMT/<strong><strong><strong><br />
</strong></strong></strong>[8] S. Saitoh, A reproducing kernel theory with some general applications, Qian,T./Rodino,L.$($eds.$)$: Mathematical Analysis, Probability and Applications - Plenary Lectures: Isaac 2015, Macau, China, Springer Proceedings in Mathematics and Statistics, <strong>177</strong>$($2016$)$, 151-182 $($Springer$)$.<strong><strong><strong><br />
</strong></strong></strong>[9] S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operations on the real and complex fields, Tokyo Journal of Mathematics, <strong>38</strong>$($2015$)$, no. 2, 369-380.<strong><strong><strong><br />
</strong></strong></strong>[10] Announcement 179 $($2014.8.30$)$: Division by zero is clear as z/0=0 and it is fundamental in mathematics.<br />
[11] Announcement 185 $($2014.10.22$)$: The importance of the division by zero $z/0=0$.<br />
[12] Announcement 237 $($2015.6.18$)$: A reality of the division by zero $z/0=0$ by geometrical optics.<br />
[13] Announcement 246 $($2015.9.17$)$: An interpretation of the division by zero $1/0=0$ by the gradients of lines.<br />
[14] Announcement 247 $($2015.9.22$)$: The gradient of y-axis is zero and $\tan (\pi/2) =0$ by the division by zero $1/0=0$.<br />
[15] Announcement 250 $($2015.10.20$)$: What are numbers? - the Yamada field containing the division by zero $z/0=0$.<br />
[16] Announcement 252 $($2015.11.1$)$: Circles and curvature - an interpretation by Mr. Hiroshi Michiwaki of the division by zero $r/0 = 0$.<br />
[17] Announcement 281 $($2016.2.1$)$: The importance of the division by zero $z/0=0$.<br />
[18] Announcement 282 $($2016.2.2$)$: The Division by Zero $z/0=0$ on the Second Birthday.<br />
[19] Announcement 293 $($2016.3.27$)$: Parallel lines on the Euclidean plane from the viewpoint of division by zero 1/0=0.<br />
[20] Announcement 300 $($2016.05.22$)$: New challenges on the division by zero z/0=0.<br />
[21] Announcement 326 $($2016.10.17$)$: The division by zero z/0=0 - its impact to human beings through education and research.<br />
[22] Announcement 352 $($2017.2.2$)$: On the third birthday of the division by zero z/0=0.<br />
[23] Announcement 354 $($2017.2.8$)$: What are $n = 2,1,0$ regular polygons inscribed in a disc? -- relations of $0$ and infinity.<br />
[24] Announcement 362$($2017.5.5$)$: Discovery of the division by zero as $0/0=1/0=z/0=0$.<br />
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http://okmr.yamatoblog.net/division%20by%20zero/announcement%20380-%20%20%20what%20i