2018年12月22日土曜日

National Mathematics Day 2018: Why it is celebrated; Srinivasa Ramanujan's life, acheivements

National Mathematics Day 2018: Why it is celebrated; Srinivasa Ramanujan's life, acheivements


Tomorrow (December 22) is the National Mathematics Day. It is observed to honor the birth anniversary of the famous mathematician Srinivasa Ramanujan who greatly contributed towards mathematical analysis, number theory, infinite series and continued fractions. Ramanujan lived during the British Rule in India. He died at a young age of 32 in London on 26 April 1920. He had almost no formal training in pure mathematics. Mathematician Srinivasa Ramanujan (Image credit - Youtube screengrab) During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations). Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research. Highlights of Srinivasa Ramanujan's life: In 1911, Ramanujan published the first of his papers in the Journal of the Indian Mathematical Society. Ramanujan's genius slowly gained recognition, and in 1913 he began a correspondence with the British mathematician Godfrey H. Hardy that led to a special scholarship from the University of Madras and a grant from Trinity College, Cambridge. Ramanujan traveled to England in 1914, where Hardy tutored him and collaborated with him in some research. He worked out the Riemann series, the elliptic integrals, hypergeometric series, the functional equations of the zeta function, and his own theory of divergent series. The number 1729 is known as the Hardy-Ramanujan number after a famous visit by Hardy to see Ramanujan at a hospital. Hardy observed Ramanujan's work primarily involved fields less known even amongst other pure mathematicians. National Mathematics Day: In 2011, on the 125th anniversary of his birth, the Indian Government declared that 22 December will be celebrated every year as National Mathematics Day.[75] Then Indian Prime Minister Manmohan Singh also declared that the year 2012 would be celebrated as the National Mathematics Year. he great Indian mathematicians such as Brahmagupta, Aryabhata, and Srinivasa Ramanujan have played a significant role in developing different formulas, theorems and theories on mathematics in India. And thus, it is important to promote and cultivate the magnificent tradition of Indian mathematics by celebrating National Mathematics Day. Srinivasa Ramanujan's life: Ramanujan was born in 1887 in Erode, Tamil Nadu, into an orthodox Iyengar Brahmin family. Ramanujan lived a life that was devoted to mathematics in all its passion. At a fledgling age of 11, Ramanujan began to show signs of an unfolding genius. By the age of 12, he had mastered trigonometry and developed many theorems on his own with no assistance. Ramanujan spent nearly five years in Cambridge collaborating with Hardy and Littlewood, and published part of his findings there. Ramanujan was awarded a Bachelor of Science degree by research (this degree was later renamed PhD) in March 1916 for his work on highly composite numbers, the first part of which was published as a paper in the Proceedings of the London Mathematical Society. The paper was more than 50 pages and proved various properties of such numbers. Throughout his life, Ramanujan was plagued by health problems. His health worsened in England; possibly he was also less resilient due to the difficulty of keeping to the strict dietary requirements of his religion in England and wartime rationing during 1914-1918. He was diagnosed with tuberculosis and a severe vitamin deficiency at the time, and was confined to a sanatorium. In 1919 he returned to Kumbakonam, Madras Presidency, and soon thereafter, in 1920, died at the age of 32.

Read more at: https://www.oneindia.com/india/national-mathematics-day-2018-why-it-is-celebrated-srinivasa-ramanujan-s-life-acheivements-2825938.html
Wasan Geometry and Division by Zero Calculus
2018年11月28日(水) テーマ:数学
Sangaku Journal of Mathematics (SJM) ⃝c SJM ISSN 2534-9562 Volume 2 (2018), pp. 57-73 Received 20 November 2018. Published on-line 29 November 2018 web: http://www.sangaku-journal.eu/ ⃝c The Author(s) This article is published with open access1 . Wasan Geometry and Division by Zero Calculus
file:///C:/Users/saito%20saburo/Downloads/SJM_2018_57-73_okumura_saitoh%20(1).pdf
               
ゼロ除算の発見は日本です:
∞???   
∞は定まった数ではない・・・・
人工知能はゼロ除算ができるでしょうか:
とても興味深く読みました:2014年2月2日 4周年を超えました:
ゼロ除算の発見と重要性を指摘した:日本、再生核研究所

\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,amssymb,amsfonts,amstext,amsthm}
\numberwithin{equation}{section}
\begin{document}
\title{\bf  Announcement 412:  The 4th birthday of the division by zero $z/0=0$ \\
(2018.2.2)}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
 }
\date{\today}
\maketitle
 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 Aristotelēs (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 Brāhmasphuṭasiddhānta (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 \cite{s18} with 154 pages
 and stated in the preface and last section of the manuscript as follows:
\bigskip


{\bf Preface}
\medskip

 The division by zero has a long and mysterious story over the world (see, for example, H. G. Romig \cite{romig} 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.

 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 $z =b/a$.

  However, the result (definition) will show that
      for the elementary mapping
\begin{equation}
W = \frac{1}{z},
\end{equation}
the image of $z=0$ is $W=0$ ({\bf 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 (\cite{ahlfors}). �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 {\bf continuity} with the common sense or
based on the basic idea of Aristotle.  --
 For the related Greece philosophy, see \cite{a,b,c}. 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  (\cite{mos,osm}) 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.

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.

\bigskip
\bigskip

{\bf Conclusion}
\medskip


 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.

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.

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 \cite{guan} since 30 years proposed  in \cite{s88} (the original is in \cite {s79}).

We have to arrange globally our modern mathematics with our division by zero  in our undergraduate level.

We have to change our basic ideas for our space and world.

We have to change globally our textbooks and scientific books on the division by zero.






\bibliographystyle{plain}
\begin{thebibliography}{10}

\bibitem{ahlfors}
L. V. Ahlfors, Complex Analysis, McGraw-Hill Book Company, 1966.


\bibitem{cs}
L. P.  Castro and S. Saitoh,  Fractional functions and their representations,  Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.

\bibitem{guan}
Q.  Guan,  A proof of Saitoh's conjecture for conjugate Hardy H2 kernels, arXiv:1712.04207.


\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{ms16}
T. Matsuura and S. Saitoh,
Matrices and division by zero z/0=0,
Advances in Linear Algebra \& Matrix Theory, {\bf 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.

\bibitem{ms18}
T. Matsuura and S. Saitoh,
Division by zero calculus and singular integrals. (Submitted for publication)

\bibitem{mms18}
T. Matsuura, H. Michiwaki and S. Saitoh,
$\log 0= \log \infty =0$ and applications. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics.

\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. {\bf 6}(2015), 1--8. http://www.ijapm.org/show-63-504-1.html

\bibitem{mos}
H. Michiwaki, H. Okumura and S. Saitoh,
 Division by Zero $z/0 = 0$ in Euclidean Spaces,
 International Journal of Mathematics and Computation, {\bf 2}8(2017); Issue  1, 2017), 1-16.


\bibitem{osm}
H. Okumura, S. Saitoh and T. Matsuura, Relations of   $0$ and  $\infty$,
Journal of Technology and Social Science (JTSS), {\bf 1}(2017),  70-77.

\bibitem{os}
H. Okumura and S. Saitoh, The Descartes circles theorem and division by zero calculus. https://arxiv.org/abs/1711.04961 (2017.11.14).

\bibitem{o}
H. Okumura, Wasan geometry with the division by 0. https://arxiv.org/abs/1711.06947 International  Journal of Geometry.

\bibitem{os18}
H. Okumura and S. Saitoh,
Applications of the division by zero calculus to Wasan geometry.
(Submitted for publication).

\bibitem{ps18}
S. Pinelas and S. Saitoh,
Division by zero calculus and differential equations. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics.

\bibitem{romig}
H. G. Romig, Discussions: Early History of Division by Zero,
American Mathematical Monthly, Vol. {\bf 3}1, No. 8. (Oct., 1924), pp. 387-389.


\bibitem{s79}
S. Saitoh, The Bergman norm and the Szeg$\ddot{o}$ norm, Trans. Amer. Math. Soc. {\bf 249} (1979), no. 2, 261--279.

\bibitem{s88}
 S. Saitoh, Theory of reproducing kernels and its applications. Pitman Research Notes in Mathematics Series, {\bf 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

\bibitem{s14}
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{s16}
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,  {\bf 177}(2016),     151-182. (Springer) .

\bibitem{s17}
S. Saitoh, Mysterious Properties of the Point at Infinity、
arXiv:1712.09467 [math.GM](2017.12.17).

\bibitem{s18}
S. Saitoh, Division by zero calculus (154 pages: draft): (http://okmr.yamatoblog.net/)

\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{a}
https://philosophy.kent.edu/OPA2/sites/default/files/012001.pdf

\bibitem{b}
http://publish.uwo.ca/~jbell/The 20Continuous.pdf

\bibitem{c}
http://www.mathpages.com/home/kmath526/kmath526.htm



\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{ann281}
Announcement 281 (2016.2.1): The importance of the division by zero $z/0=0$.

\bibitem{ann282}
Announcement 282 (2016.2.2): The Division by Zero $z/0=0$ on the Second Birthday.

\bibitem{ann293}
Announcement 293 (2016.3.27):  Parallel lines on the Euclidean plane from the viewpoint of division by zero 1/0=0.

\bibitem{ann300}
Announcement 300 (2016.05.22): New challenges on the division by zero z/0=0.

\bibitem{ann326}
 Announcement 326 (2016.10.17): The division by zero z/0=0 - its impact to human beings through education and research.

 \bibitem{ann352}
Announcement 352(2017.2.2):   On the third birthday of the division by zero z/0=0.

\bibitem{ann354}
Announcement 354(2017.2.8): What are $n = 2,1,0$ regular polygons inscribed in a disc? -- relations of $0$ and infinity.

\bibitem{362}
Announcement 362(2017.5.5): Discovery of the division by zero as  $0/0=1/0=z/0=0$

 \bibitem{380}
Announcement 380 (2017.8.21):  What is the zero?

\bibitem{388}
Announcement 388(2017.10.29):   Information and ideas on zero and division by zero (a project).

 \bibitem{409}
Announcement 409 (2018.1.29.):  Various Publication Projects on the Division by Zero.

\bibitem{410}
Announcement 410 (2018.1 30.):  What is mathematics? -- beyond logic; for great challengers on the division by zero.


\end{thebibliography}

\end{document}


List of division by zero:

\bibitem{os18}
H. Okumura and S. Saitoh,
Remarks for The Twin Circles of Archimedes in a Skewed Arbelos by H. Okumura and M. Watanabe, Forum Geometricorum.

Saburou Saitoh, Mysterious Properties of the Point at Infinity、
arXiv:1712.09467 [math.GM]

Hiroshi Okumura and Saburou Saitoh
The Descartes circles theorem and division by zero calculus. 2017.11.14

L. P. Castro and S. Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.

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.

T. Matsuura and S. Saitoh,
Matrices and division by zero z/0=0,
Advances in Linear Algebra \& Matrix Theory, 2016, 6, 51-58
Published Online June 2016 in SciRes. http://www.scirp.org/journal/alamt
\\ http://dx.doi.org/10.4236/alamt.2016.62007.

T. Matsuura and S. Saitoh,
Division by zero calculus and singular integrals. (Submitted for publication).

T. Matsuura, H. Michiwaki and S. Saitoh,
$\log 0= \log \infty =0$ and applications. (Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics.)

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

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, 2017), 1-16.

H. Okumura, S. Saitoh and T. Matsuura, Relations of $0$ and $\infty$,
Journal of Technology and Social Science (JTSS), 1(2017), 70-77.

S. Pinelas and S. Saitoh,
Division by zero calculus and differential equations. (Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics).

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/

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, {\bf 177}(2016), 151-182. (Springer) .


再生核研究所声明371(2017.6.27)ゼロ除算の講演― 国際会議 https://sites.google.com/site/sandrapinelas/icddea-2017 報告


1/0=0、0/0=0、z/0=0
http://ameblo.jp/syoshinoris/entry-12276045402.html
1/0=0、0/0=0、z/0=0
http://ameblo.jp/syoshinoris/entry-12263708422.html
1/0=0、0/0=0、z/0=0

ソクラテス・プラトン・アリストテレス その他


Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.

私は数学を信じない。 アルバート・アインシュタイン / I don't believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。

ドキュメンタリー 2017: 神の数式 第2回 宇宙はなぜ生まれたのか


〔NHKスペシャル〕神の数式 完全版 第3回 宇宙はなぜ始まったのか


〔NHKスペシャル〕神の数式 完全版 第1回 この世は何からできているのか

NHKスペシャル 神の数式 完全版 第4回 異次元宇宙は存在するか

                                                 
再生核研究所声明 411(2018.02.02):  ゼロ除算発見4周年を迎えて

ゼロ除算の論文

Mysterious Properties of the Point at Infinity

Algebraic division by zero implemented as quasigeometric multiplication by infinity in real and complex multispatial hyperspaces
Author: Jakub Czajko, 92(2) (2018) 171-197
https://img-proxy.blog-video.jp/images?url=http%3A%2F%2Fwww.worldscientificnews.com%2Fwp-content%2Fplugins%2Ffiletype-icons%2Ficons%2F16%2Ffile_extension_pdf.pngWSN 92(2) (2018) 171-197
                                                                                                                                             

2018.3.18.午前中 最後の講演: 日本数学会 東大駒場、函数方程式論分科会 講演書画カメラ用 原稿
The Japanese Mathematical Society, Annual Meeting at the University of Tokyo. 2018.3.18.
https://ameblo.jp/syoshinoris/entry-12361744016.html より


*057  Pinelas,S./Caraballo,T./Kloeden,P./Graef,J.(eds.):
       Differential and Difference Equations with Applications:
        ICDDEA, Amadora, 2017.
           (Springer Proceedings in Mathematics and Statistics, Vol. 230)
             May 2018       587 pp. 


ゼロ除算の論文が2編、出版になりました:

ICDDEA: International Conference on Differential & Difference Equations and Applications
Differential and Difference Equations with Applications
ICDDEA, Amadora, Portugal, June 2017
• Editors

• (view affiliations)
• Sandra Pinelas
• Tomás Caraballo
• Peter Kloeden
• John R. Graef
Conference proceedingsICDDEA 2017

log0=log∞=0log⁡0=log⁡∞=0 and Applications
Hiroshi Michiwaki, Tsutomu Matuura, Saburou Saitoh
Pages 293-305

Division by Zero Calculus and Differential Equations
Sandra Pinelas, Saburou Saitoh
Pages 399-418

ゼロ除算(division by zero)1/0=0、0/0=0、z/0=0

2018年05月28日(月)
テーマ:数学
これは最も簡単な 典型的なゼロ除算の結果と言えます。 ユークリッド以来の驚嘆する、誰にも分る結果では ないでしょうか?
                                                                      
Hiroshi O. Is It Really Impossible To Divide By Zero?. Biostat Biometrics Open Acc J. 2018; 7(1): 555703.  DOI: 10.19080/BBOJ.2018.07.555703
ゼロで分裂するのは本当に不可能ですか? - Juniper Publishers         


再生核研究所 ゼロ除算の発見と重要性を指摘した:2014年2月2日

神の数式で ゼロ除算を用いると どうなるのでしょうか という質問が 寄せられています。
神の数式:
神の数式が解析関数でかけて居れば、 特異点でローラン展開して、正則部の第1項を取れば、 何時でも有限値を得るので、 形式的に無限が出ても 実は問題なく 意味を有します。
物理学者如何でしょうか。

計算機は 正しい答え 0/0=0 を出したのに計算機は何時、1/0=0 ができるようになるでしょうか。
 
カテゴリ:カテゴリ未分類
そこで、計算機は何時、1/0=0 ができるようになるでしょうか。 楽しみにしています。 もうできる進化した 計算機をお持ちの方は おられないですね。
これは凄い、面白い事件では? 計算機が人間を超えている 例では?

面白いことを発見しました。 計算機は 正しい答え 0/0=0
を出したのに、 この方は 間違いだと 言っている、思っているようです。
0/0=0 は 1300年も前に 算術の発見者によって与えられたにも関わらず、世界史は間違いだと とんでもないことを言ってきた。 世界史の恥。 実は a/0=0 が 何時も成り立っていた。 しかし、ここで 分数の意味を きちんと定義する必要がある。 計算機は、その意味さえ知っているようですね。 計算機、人間より賢くなっている 様が 出て居て 実に 面白い。
https://steemkr.com/utopian-io/@faisalamin/bug-zero-divide-by-zero-answers-is-zero
2018.10.11.11:23
https://plaza.rakuten.co.jp/reproducingkerne/diary/201810110003/
計算機は 正しい答え 0/0=0 を出したのに
カテゴリ:カテゴリ未分類

面白いことを発見しました。 計算機は 正しい答え 0/0=0
を出したのに、 この方は 間違いだと 言っている、思っているようです。
0/0=0 は 1300年も前に 算術の発見者によって与えられたにも関わらず、世界史は間違いだと とんでもないことを言ってきた。 実は a/0=0 が 何時も成り立っていた。しかし、ここで 分数の意味を きちんと定義する必要がある。 計算機は、その意味さえ知っているようですね。 計算機、人間より賢くなっている様が 出て居て 実に面白い。


https://steemkr.com/utopian-io/@faisalamin/bug-zero-divide-by-zero-answers-is-zero
2018.10.11.11:23

ゼロ除算、ゼロで割る問題、分からない、正しいのかなど、 良く理解できない人が 未だに 多いようです。そこで、簡潔な一般的な 解説を思い付きました。 もちろん、学会などでも述べていますが、 予断で 良く聞けないようです。まず、分数、a/b は a  割る b のことで、これは 方程式 b x=a の解のことです。ところが、 b がゼロならば、 どんな xでも 0 x =0 ですから、a がゼロでなければ、解は存在せず、 従って 100/0 など、ゼロ除算は考えられない、できないとなってしまいます。 普通の意味では ゼロ除算は 不可能であるという、世界の常識、定説です。できない、不可能であると言われれば、いろいろ考えたくなるのが、人間らしい創造の精神です。 基本方程式 b x=a が b がゼロならば解けない、解が存在しないので、困るのですが、このようなとき、従来の結果が成り立つような意味で、解が考えられないかと、数学者は良く考えて来ました。 何と、 そのような方程式は 何時でも唯一つに 一般化された意味で解をもつと考える 方法があります。 Moore-Penrose 一般化逆の考え方です。 どんな行列の 逆行列を唯一つに定める 一般的な 素晴らしい、自然な考えです。その考えだと、 b がゼロの時、解はゼロが出るので、 a/0=0 と定義するのは 当然です。 すなわち、この意味で 方程式の解を考えて 分数を考えれば、ゼロ除算は ゼロとして定まる ということです。ただ一つに定まるのですから、 この考えは 自然で、その意味を知りたいと 考えるのは、当然ではないでしょうか?初等数学全般に影響を与える ユークリッド以来の新世界が 現れてきます。
ゼロ除算の誤解は深刻:

最近、3つの事が在りました。

私の簡単な講演、相当な数学者が信じられないような誤解をして、全然理解できなく、目が回っているいるような印象を受けたこと、
相当ゼロ除算の研究をされている方が、基本を誤解されていたこと、1/0 の定義を誤解されていた。
相当な才能の持ち主が、連続性や順序に拘って、4年以上もゼロ除算の研究を避けていたこと。

これらのことは、人間如何に予断と偏見にハマった存在であるかを教えている。
まずは ゼロ除算は不可能であるの 思いが強すぎで、初めからダメ、考えない、無視の気持ちが、強い。 ゼロ除算を従来の 掛け算の逆と考えると、不可能であるが 証明されてしまうので、割り算の意味を拡張しないと、考えられない。それで、 1/0,0/0,z/0 などの意味を発見する必要がある。 それらの意味は、普通の意味ではないことの 初めの考えを飛ばして ダメ、ダメの感情が 突っ走ている。 非ユークリッド幾何学の出現や天動説が地動説に変わった世界史の事件のような 形相と言える。
2018.9.22.6:41
ゼロ除算の4つの誤解:
1.      ゼロでは割れない、ゼロ除算は 不可能である との考え方に拘って、思考停止している。 普通、不可能であるは、考え方や意味を拡張して 可能にできないかと考えるのが 数学の伝統であるが、それができない。
2.      可能にする考え方が 紹介されても ゼロ除算の意味を誤解して、繰り返し間違えている。可能にする理論を 素直に理解しない、 強い従来の考えに縛られている。拘っている。
3.      ゼロ除算を関数に適用すると 強力な不連続性を示すが、連続性のアリストテレス以来の 連続性の考えに囚われていて 強力な不連続性を受け入れられない。数学では、不連続性の概念を明確に持っているのに、不連続性の凄い現象に、ゼロ除算の場合には 理解できない。
4.      深刻な誤解は、ゼロ除算は本質的に定義であり、仮定に基づいているので 疑いの気持ちがぬぐえず、ダメ、怪しいと誤解している。数学が公理系に基づいた理論体系のように、ゼロ除算は 新しい仮定に基づいていること。 定義に基づいていることの認識が良く理解できず、誤解している。
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.



Eπi =-1 (1748)(Leonhard Euler)
E = mc 2 (1905)(Albert Einstein)
1/0=0/0=0 (2014年2月2日再生核研究所)

ゼロ除算(division by zero)1/0=0/0=z/0= tan (pi/2)=0
https://ameblo.jp/syoshinoris/entry-12420397278.html


1+1=2  (      )
a2+b2=c2 (Pythagoras)
1/0=0/0=0(2014年2月2日再生核研究所)




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