ＡＩブームまだ終わらず、「新たな産業革命」
https://jp.reuters.com/
想像以上に進んでいます。
ChatGPT等での推論モデル拡大、
https://news.yahoo.co.jp/
エヌビディア決算、売上高・最終利益ともに過去最高…
https://www.yomiuri.co.jp/
科学を変えた10のコンピューターコード
Fortranからプレプリントアーカイブまで、
【無料公開】世界を変えた7つの偉大な「方程式」、
https://diamond.jp/articles/-/
【無料】数学の問題を解いてくれるアプリおすすめ５選！
https://www.perfectcorp.com/
安野貴博に聞く、社会の常識が変わるAI時代に「変化」を「
https://article.yahoo.co.jp/
世界を変えたすべての方程式のタイムライン
https://www.youtube.com/watch?
1/Z＝0の方程式の解は何ですか。
全知全能の最先端AI「Cristal」が企業の大脳となる ソフトバンク孫正義氏が語る、現代における「超知性」の可能性
https://logmi.jp/main/
Monica
Instant
要約マインドマップ
ゼロ除算の定義 ゼロ除算は、ある数を0で割ることを指し、
ゼロ除算算法の概念 ゼロ除算算法は、
ゼロ除算に関する議論 現在、
２０１４年２月２日ゼロ除算の発見
２０１４年３月８日ゼロ除算算法の発見
２０２５年１月１４日ゼロベクトルの方向の発見
「恐ろしく賢い」とマスクが評するxAIのチャットボットGrok 3、18日発表
https://news.yahoo.co.jp/articles/211bfb6c1ea87172d539e730837b6d1fcbdece91
マスク氏、対話型ＡＩ「グロック３」をリリース 日本時間18日午後1時
https://jp.reuters.com/business/technology/2H77L2RUWZIV3DPPQOBPBTQ6ZE-2025-02-16/
ゼロ除算は、解決したと言われていますが、どのような状況でしょうか。
再生核研究所声明 424(2018.3.29): レオナルド・ダ・ヴィンチとゼロ除算
次のダ・ヴィンチの言葉を発見して、驚かされた：
ダ・ヴィンチの名言 格言｜無こそ最も素晴らしい存在
我々の周りにある偉大なことの中でも、無の存在が最も素晴らしい。その基本は時間的には過去と未来の間にあり、現在の何ものをも所有しないというところにある。この無は、全体に等しい部分、部分に等しい全体を持つ。分割できないものと割り切ることができるし、割っても掛けても、足しても引いても、同じ量になるのだ。
レオナルド・ダ・ヴィンチ。ルネッサンス期を代表する芸術家、画家、彫刻家、建築技師、設計士、兵器開発者、科学者、哲学者、解剖学者、動物学者、ファッションデザイナーその他広い分野で活躍し「万能の人（uomo universale：ウォモ・ウニヴェルサーレ）」と称えられる人物
https://systemincome.com/7521 https://todays-list.com/i/?q=/ucaggsehdbgf/1/4/
そもそも西欧諸国が、アリストテレス以来、無や真空、ゼロを嫌い、ゼロの西欧諸国への導入は相当に遅れ、西欧へのアラビヤ数字の導入は レオナルド・フィボナッチ（1179年頃～1250年頃）によるとされているから、その遅れの大きさに驚かされる：
フィボナッチはイタリアのピサの数学者です。正確には「レオナルド・フィリオ・ボナッチ」といいますが、これがなまって「フィボナッチ」と呼ばれるようになったとされています。
彼は少年時代に父親について現在のアルジェリアに渡り、そこでアラビア数字を学びました。当時の神聖ローマ皇帝・フリードリヒ2世は科学と数学を重んじていて、フィボナッチは宮殿に呼ばれ皇帝にも謁見しました。後にはピサ共和国から表彰もされました。
ローマ数字では「I, II, III, X, XV」のように文字を並べて記すため大きな数を扱うのには不便でした。対してアラビア数字はローマ数字に比べてとても分かりやすく、効率的で便利だったのです。そこでフィボナッチはアラビア数字を「算術の書」という書物にまとめ、母国に紹介しました。アラビア数字では0から9までの数字と位取り記数法が使われていますが、計算に使うにはとても便利だったために、ヨーロッパで広く受け入れられることになりました。（歴史上の数学者たち: レオナルド・フィボナッチ
historicalmathematicians.blogspot.com/2012/03/blog-post.html Traduzir esta página 02/03/2012 -）
ゼロや無に対する恐怖心、嫌疑観は現在でも欧米諸国の自然な心情と考えられる。ところが上記ダ・ヴィンチの言葉は 如何であろう。無について好ましいものとして真正面から捉えていることが分かる。ゼロ除算の研究をここ４年間して来て、驚嘆すべきこととして驚かされた。ゼロの意味、ゼロ除算の心を知っていたかのような言明である。
まず、上記で、無を、時間的に未来と過去の間に存在すると言っているので、無とはゼロのことであると解釈できる。ゼロとの捉え方は四則演算を考えているので、その解釈の適切性を述べている。足しても引いても変わらない。これはゼロの本質ではないか。さらに、凄いこと、掛けても割っても、ゼロと言っていると解釈でき、それはゼロ除算の最近の発見を意味している: 0/1 =1/0=0。－ ゼロ除算を感覚的に捉えていたと解釈できる。ところが更に、凄いことを述べている。
この無は、全体に等しい部分、部分に等しい全体を持つ。これはゼロ除算の著書DIVISION BY ZERO CALCULUS（原案）に真正面から書いている我々の得た、達したゼロに対する認識そのものである：
{\bf Fruitful world}\index{fruitful world}
\medskip
For example, in very and very general partial differential equations, if the coefficients or terms are zero, 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 see the converse, we see that the zero world is a fruitful one and it means some vanishing world. Recall \index{Yamane phenomena}Yamane phenomena, 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 some changes as in the Yamane phenomena.
\medskip
{\bf From $0$ to $0$; $0$ means all and all are $0$}
\medskip
As we see from our life figure, a story starts from the zero and ends to the zero. This will mean that $0$ means all and all are $0$, in a sense. The zero is a mother of all.
\medskip
その意味は深い。我々はゼロの意味をいろいろと捉え考え、ゼロとはさらに 基準を表すとか、不可能性を示すとか、無限遠点の反映であるとか、ゼロの2重性とかを述べている。ゼロと無限の関係をも述べている。ダ・ヴィンチの鋭い世界観に対する境地に驚嘆している。
以 上
*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
Reproducing Kernel Research Institute Statement 424 (2018.3.29): Leonardo da Vinci and division by zero
I was surprised to discover the following Da Vinci's words:
Da Vinci's Quotations Quotations | Nothing is the Most Wonderful
Of all the great things around us, the existence of nothingness is the most wonderful. The basis is that it is between the past and the future in terms of time, and that it owns nothing of the present. This nothing has a part equal to the whole and a whole equal to the part. You can divide it into something that cannot be divided, and even if you divide it, multiply it, add it, or subtract it, the amount will be the same.
Leonardo da Vinci. An artist, painter, sculptor, architectural engineer, designer, weapons developer, scientist, philosopher, anatomist, zoologist, fashion designer, and other representative artists of the Renaissance period. : Womo Universale) "
https://systemincome.com/7521 https://todays-list.com/i/?q=0ucaggsehdbgf/1/4/
In the first place, Western countries have hated nothing, vacuum, and zero since Aristotelis, the introduction of zero to Western countries has been considerably delayed, and the introduction of Arabic numbers to Western Europe is according to his Leonardo Fibonacci (c. 1179 to 1250). Being surprised by the magnitude of the delay:
Fibonacci is an Italian mathematician in Pisa. To be precise, it is called "Leonardo Fibonacci", but it is said that this became known as "Fibonacci".
He traveled to what is now Algeria about his father during his childhood, where he studied Arabic numerals. The Holy Roman Emperor Frederick II at that time valued science and mathematics, and Fibonacci was called to the palace and had an audience with the emperor. He was later commended by the Republic of Pisa.
In Roman numerals, it was inconvenient to handle large numbers because the letters were written side by side, such as "I, II, III, X, XV". Arabic numerals, on the other hand, were much easier to understand, more efficient and more convenient than Roman numerals. So Fibonacci compiled Arabic numerals into a book called "The Book of Arithmetic" and introduced it to his home country. Arabic numerals use numbers from 0 to 9 and the scale notation system, but they were so convenient to use in their calculations that they became widely accepted in Europe. (Historical mathematicians: Leonardo Fibonacci
historicalmathematicians.blogspot.com/2012/03/blog-post.html Traduzir esta página 02/03/2012-)
Fear and suspicion of zero and nothing are still considered to be the natural feelings of Western countries. However, what is Da Vinci's words above? It can be seen that nothing is viewed head-on as a favorable one. I've been studying division by zero for the last four years and was amazed at how amazing it was. It is a statement as if he knew the meaning of zero and the mind of division by zero.
First, since we say that nothing exists between the future and the past in terms of time, we can interpret nothing as zero. Since the way of thinking as zero considers four arithmetic operations, it states the appropriateness of its interpretation. It doesn't change whether you add or subtract. Isn't this the essence of zero? What's more, it can be interpreted as zero, whether multiplied or divided, which means the recent discovery of division by zero: 0/1 = 1/0 = 0. -It can be interpreted that the division by zero was perceived sensuously. However, he also states something amazing.
This nothing has a part equal to the whole and a whole equal to the part. This is the very recognition of zero that we have gained, which we wrote head-on in the division by zero book DIVISION BY ZERO CALCULUS:
{\ bf Fruitful world} \ index {fruitful world}
\ medskip
For example, in very and very general partial differential equations, if the coefficients or terms are zero, 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 Recall \ index {Yamane phenomena} Yamane phenomena, the vanishing result is very simple zero, however, it is sometimes, zero means void or nothing world, however, it will show some changes as in the Yamane phenomena.
\ medskip
{\ bf From $ 0 $ to $ 0 $; $ 0 $ means all and all are $ 0 $}
\ medskip
As we see from our life figure, a story starts from the zero and ends to the zero. This will mean that $ 0 $ means all and all are $ 0 $, in a sense. The zero is a mother of all.
\ medskip
The meaning is deep. We think about the meaning of zero in various ways, and further state that zero represents a standard, indicates impossibility, reflects the point at infinity, and is the duality of zero. It also states the relationship between zero and infinity. I am amazed at Da Vinci's sharp view of the world.
that's all
* 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.
世界の偉人ランキングTOP２０【尊敬する歴史上の人物とは？】
目次
- ２０位：バッハ（作曲家）
- １９位：トーマス・ジェファーソン（政治家）
- １８位：カント（哲学者）
- １７位：シェイクスピア（作家）
- １６位：ピタゴラス（数学者）
- １５位：コペルニクス（天文学者）
- １４位：ケプラー（天文学者）
- １３位：フランクリン（政治家・物理学者）
- １２位：ダーウィン（生物学者）
- １１位：マリ・キュリー（物理学者・化学者）
- １０位：ミケランジェロ（彫刻家・建築家）
- ９位：アルキメデス（数学者・発明家）
- ８位：ニコラ・テスラ（電気技師・発明家）
- ７位：モーツァルト（作曲家）
- ６位：プラトン（哲学者）
- ５位：アインシュタイン（物理学者）
- ４位：アリストテレス（哲学者）
- ３位：ガリレオ（天文学者）
- ２位：ニュートン（物理学者・数学者）
- １位：ダ・ヴィンチ（美術家・科学者・数学者・発明家）
- 世界偉人ランキングにおける不動のチャンピオン：イエス・キリスト
https://hotnews8.net/human/greatest-mind-ranking
Statement 520 (December 04, 2019): Mathematics Super Difficult-Division by Zero-Solved
On a special day, I was having breakfast with my family at 6:00 on the 3rd. Suddenly, the title and concept came to me, so I want to express it in a funny and frank way.
First of all, I would like to explain the meaning of the super-difficult problem. I would like to briefly explain how division by zero was a difficult problem in the first place. Aristotle, such as Thales, he did before, he did, and he hated zero in Greek and Western cultures with nothing and the sky, and some experts thought that Aristotle was not divisible by zero, and had a long-standing influence. Has been given.
On the other hand, in India, from ancient times, the idea of nothingness and the sky was obtained, and the concept of zero was obtained, but the founder of arithmetic, Brahmagupta (598 --- 668?), Obtained 0/0 = 0. Without mentioning general zero division, I have continued to make mistakes 1/0 = INFINITY ∞ since Baskara II (1114-1185).
This result is also famous as a famous mistake of genius Euler.
Of course, his division by zero clearly appeared in Newton's Law of Universal Gravity, the finest physicist in history, allegedly his lifelong task:
Blackholes are where God divided by zero.
I don't believe in mathematics.
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} Gamow, G., My World Line (Viking, New York). P 44, 1970).
Early Modern Mathematics Over 200 Years It is clear that the world of mathematics does not recognize division by zero because the problem of division by zero is impossible in the ordinary sense, and does not consider the problem itself:
S. K. Sen and R. P. Agarwal (2016): First of the Ten Commandments of Mathematics, Thou shalt not divide by zero:
{\ bf “Thou shalt not divide by zero” remains valid eternally.}
However, the problem of dividing by zero is mainly a research of division by zero as an inherent problem, from the viewpoint of the theory of relativity and division by zero, and as a logical problem in the wake of the case where division by zero caused a computer failure. It has been enthusiastically studied by physicists other than mathematicians and those involved in computers. However, it is thought that those enormous amounts of research are no longer available.
There is an interesting case, so I would like to mention it:
L. C. Paulson stated that I would guess that Isabelle has used this {\ bf convention} $ 1/0 = 0 $ since the 1980s and introduced his book her referred to this fact.
However, in his group her importance of this fact seems to be entirely ignored at this moment as we see from the book.
He is currently one of the heads of Isabelle / HOL, and the above is part of his email, but I think the system has issued his 1/0 = 0 for 40 years, which means I don't know, and I don't seem to recognize its importance. This fact is also reflected in his recent treatise on division by zero. -What's really interesting is
He seems to have been unaware of its meaning and importance by humans, even though the calculator was producing correct and legitimate results.
Then, using his advanced computer system, Jose examines the division by zero and division by zero we have obtained, giving us a strong guarantee of our results. -Division by zero is possible in a new sense, claiming that the new world has opened up the world since Aristotle and Euclid, and is seeking widespread opinion:
Thou shalt not divide by zero The Ten Commandments of the Ten Commandments have been overturned, and by dividing by zero, a new world has emerged, which can be divided by zero, the new mathematics since Aristotle and Euclid, the new world has emerged. A symbolic example is
1/0 = 0/0 = z / 0 = tan (\ pi / 2) = log 0 = 0 and z ^ n / n = log z for n = 0.
The value at the origin of the basic function y = 1 / x is zero for him. The point at infinity is represented by zero. It is a new discovery with the meaning of zero.
These math layman's commentary is given below over his 55 months:
Foundations of Mathematics Study Group Official Website Fun Mathematics
www.mirun.sctv.jp/~suugaku/
Mathematical review papers are published below:
viXra: 1904.0408 submitted on 2019-04-22 00:32:30,
What Was Division by Zero ?; Division by Zero Calculus and New World
We state that elementary mathematics has fundamental flaws. He states that division by zero is a shame in world history, not only for mathematicians but also for humankind.
See also:
Statement of the Institute for Regenerative Nuclear Research 490: The cause and purpose of Reiwa innovation-elementary mathematics
Statement by the Institute for Regenerative Nuclear Research 493: Division by zero, answer-meaning of Reiwa innovation in elementary mathematics
Division by Zero Statement 495: Why Division by Zero is Difficult to Understand-Division by Zero Statement 493 (July 7, 2019) I don't know the answer-The pre-stage of the meaning of Reiwa innovation in elementary mathematics
Regeneration Nuclear Research Institute Statement 496 (July 7, 2019): Meaning of Reiwa Innovation in Elementary Mathematics-For the general public who dislike mathematics
Statement by the Institute for Regenerative Nuclear Research 497 (July 7, 2019): Why division by zero is difficult and why it is natural
Statement by the Institute for Regenerative Nuclear Research 498 (July 11, 2019): Why is division by zero surprising?
Statement by the Institute for Regenerative Nuclear Research 500 (July 28, 2019): Reiwa Innovation in Mathematics and Japan's Challenge, Tokyo Olympics
Ku
that's all
\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,amssymb,amsfonts,amstext,amsthm}
\numberwithin{equation}{section}
\begin{document}
\title{\bf Announcement 600: The 7th birthday of the division by zero $z/0=0$ \\
(2021.2.2)\\ For Founding a new International Journal of Division by Zero Calculus
}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
{\bf kbdmm360@yahoo.co.jp}\\
}
\date{2021.1.26.}
\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 Aristotele (BC384 - BC322) and Euclid (BC 3 Century - ), and the division by zero is since Brahmagupta (598 - 668 ?).
However, note that the division by zero $1/0=0$ having a mysterious long history was, in fact, known as the generalized Moore-Penrose solution of the fundamental equation: $ax=b$.
\medskip
The division by zero calculus is a new and fundamental concept, and it may be defined simply as follows:
\medskip
For a function $y = f(x)$ which is $n$ order differentiable at $x =a$, we will {\bf define} the value
of the function, for $n \ge 0$
$$
\frac{f(x)}{(x -a)^n}
$$
at the point $x=a$ by the value
$$
\frac{f^{(n)}(a)}{n!}.
$$
For the important case of $n=1$,
$$
\frac{f(x)}{x -a} |_{x=a} = f^\prime(a).
$$
\medskip
Look the simple evidence of its importance:
\medskip
viXra:2010.0228 submitted on 2020-10-28 21:39:06,
Division by Zero Calculus and Euclidean Geometry - Revolution in Euclidean Geometry
\medskip
Look a simple video talk for its essence at some international conference:
\medskip
https://media.cmd.gunma-u.ac.jp/media/Play/ef7ca967c3fd4dabb188128fd6038cb81d
\medskip
For the detailed information, the book will be published soon as:
\medskip
S. Saitoh, Introduction to the Division by Zero Calculus, Scientific Research Publishing (2021) (in press).
\medskip
Some publisher of London is wishing some publication of a new International Journal of Division by Zero Calculus. The topics may be identified as the division by zero calculus. However, the contents will be related to our serious problems:
\medskip
What is ZERO?
\medskip
What is Division by Zero, in some serious sense?
\medskip
The problems may be related to mathematical philosophy, long history and our culture.
The starting of the International Journal will not be still easy at this moment, however, for its importance, we would like to manage to found the new Journal in some near future. So, we will need the kind help of the leading mathematical scientists.
\medskip
How will be the related physicists?
\medskip
Computer scientists?
\medskip
We attached the journal style (in a rough way) in the below. You can express your positive suggestions and comments for the style.
For your great contributions in connection with this topics, how will be your editorial member?
However, the final decision may be done by the publisher.
We wish to have your positive answer with your valuable suggestions and comments.
If you kindly are interested in the editorial member, then please send your simple CV with your wishes for some estimation by the publisher.
Please kindly forward this announcement to your related colleagues that you think suitable persons.
\bigskip
{\it For your starting email, I think as follows:
Many thanks for your email. The journals suggested by you are very interesting and new to the subject area. We accept to publish both journals under your editorship. We need following things from your side for preparing the sample web page of the journals.
1. Aim and Scope , Instructions to Authors, List of the editorial board members, Frequency of the journal.
Of course, they are important. However, for Frequency of the journal, we should consider it in a new type. We should not loss our valuable time for us and for the authors. We all do not like to loss our time for publication and refereeing time. This will mean that we should not fix Frequency of the journal. When a paper was accepted officially, then, soon the paper should be presented on line. So, some time, we can give the number for an accepted paper. If you wish to publish the papers in some Journal style or book, you will be able to publish them in some papers with a suitable page numbers. How will be this idea?
2. The journal will be free for the readers (open Access publications). The journal will not charge any fee from the authors for getting published in the journal.
Fine: However is it possible?
3. We need some sample images from your end to prepare the cover page for the journals.
We can consider them with computer graphics.
For a paper style, how will be it in a free style, we request it PDF in order not to
loss any valuable time for us and for the authors.
I think: this is an ideal style
viXra:2010.0228 submitted on 2020-10-28 21:39:06,
Division by Zero Calculus and Euclidean Geometry - Revolution in Euclidean Geometry
The problem is no refereeing procedures. We are requested to have some authority, some check system for the paper. This is a problem only.
I think you will be able to consider new journals in this spirit.
The publisher already gave a very good sample manuscript form by LaTex; very simple way. No problem.
4. We will provide the support to the editor to check the plagiarism in the articles via turnitin software.
We will request minor corrections formally for the accepted paper.}
\bigskip
\bibliographystyle{plain}
\begin{thebibliography}{10}
\bibitem{boyer}
C. B. Boyer, An early reference to division by zero, The Journal of the American Mathematical Monthly, {\bf 50} (1943), (8), 487- 491. Retrieved March 6, 2018, from the JSTOR database.
\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{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{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. {\bf 230} (2018), 293-305.
\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, 1-16.
\bibitem{oku18}
H. Okumura, Is It Really Impossible To Divide By Zero? Biostat Biometrics Open Acc J. 2018; 7(1): 555703.
DOI: 10.19080/BBOJ.2018.07.555703.
\bibitem{o}
H. Okumura, Wasan geometry with the division by 0. https://arxiv.org/abs/1711.06947 International Journal of Geometry. {\bf 7}(2018), No. 1, 17-20.
\bibitem{ok1812}
H. Okumura,
An Analogue to Pappus Chain theorem with Division by Zero, Forum Geom., {\bf 18} (2018), 409--412.
\bibitem{okumurafield}
H. Okumura, To Divide by Zero is to Multiply by Zero, viXra: 1811.0283 submitted on 2018-11-18 20:46:54.
\bibitem{okumura19a}
H. Okumura, A Remark of the Definition of $0/0=0$ by Brahmagupta, viXra:1902.0221 submitted on 2019-02-12 23:41:31.
\bibitem{okumura20}
H. Okumura, A Chain of Circles Touching a Circle and Its Tangent and Division by Zero,
viXra:2001.0034 submitted on 2020-01-03 01:08:58.
\bibitem{okumura20b}
H. Okumura, Pappus Chain and Division by Zero, viXra:2001.0123 replaced on 2020-01-08 06:57:36.
\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{os18april}
H. Okumura and S. Saitoh,
Harmonic Mean and Division by Zero,
Dedicated to Professor Josip Pe\v{c}ari\'{c} on the occasion of his 70th birthday, Forum Geometricorum, {\bf 18} (2018), 155—159.
\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, {\bf 18}(2018), 97-100.
\bibitem{os18e}
H. Okumura and S. Saitoh,
Applications of the division by zero calculus to Wasan geometry.
GLOBAL JOURNAL OF ADVANCED RESEARCH ON CLASSICAL AND MODERN GEOMETRIES” (GJARCMG), {\bf 7}(2018), 2, 44--49.
\bibitem{os1811}
H. Okumura and S. Saitoh,
Wasan Geometry and Division by Zero Calculus,
Sangaku Journal of Mathematics (SJM), {\bf 2 }(2018), 57--73.
\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. {\bf 230} (2018), 399-418.
\bibitem{romig}
H. G. Romig, Discussions: Early History of Division by Zero,
American Mathematical Monthly, {\bf 3}1, No. 8. (Oct., 1924), 387-389.
\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.
\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.
\end{document}
カテゴリ：カテゴリ未分類
\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,amssymb,amsfonts,amstext,amsthm}
\numberwithin{equation}{section}
\begin{document}
\title{\bf Announcement 478: Who did derive first the division by zero 1/0 and the division by zero calculus $\tan(\pi/2)=0, \log 0=0$ as the outputs of a computer? \\
(2019.3.4)}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
{\bf saburou.saitoh@gmail.com}\\
}
\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 $0/0=1/0=z/0=0$ {\bf in a natural sense} on 2014.2.2. The result shows a new basic idea on the universe and space since Aristotele (BC384 - BC322) and Euclid (BC 3 Century - ), and the division by zero is since Brahmagupta (598 - 668 ?).
For the details, see the references.
A simple and essential introduction of the division by zero is given by the {\bf division by zero calculus}:
For any Laurent expansion around $z=a$,
\begin{equation} \label{dvc5.1}
f(z) = \sum_{n=-\infty}^{-1} C_n (z - a)^n + C_0 + \sum_{n=1}^{\infty} C_n (z - a)^n,
\end{equation}
we define
\begin{equation}\label{dvc5.2}
f(a) = C_0,
\end{equation}
as a value of the function $f$ at the singular point $z=a$.
For the importance of this definition, the division by zero calculus may be considered as a new axiom. This was discovered on May 8, 2014.
In particular, for the function $W= f(z) =1/z$, we have $f(0)=0$. We will write this result as
$$
\frac{1}{0}=0,
$$
from the form.
Here, the definition of $\frac{1}{0}$ is given by this sense by means of the division by zero calculus. Of course, $\frac{1}{0}$ is not a usual sense that $\frac{1}{0} =X$ if and only if $1=0 \times X$; this means a contradiction. See \cite{saitohzi} for the details.
On February 16, 2019 Professor H. Okumura introduced the surprising news in Research Gate:
\medskip
José Manuel Rodríguez Caballero\\
Added an answer\\
In the proof assistant Isabelle/HOL we have $x/0 = 0$ for each number $x$. This is advantageous in order to simplify the proofs. You can download this proof assistant here: {\bf https://isabelle.in.tum.de/}.
\medskip
J.M.R. Caballero kindly showed surprisingly several examples by the system that
$$
\tan \frac{\pi}{2} =0,
$$
$$
\log 0 =0,
$$
$$
\exp \frac{1}{x} (x=0) =1,
$$
and others. Precisely:
\medskip
Dear Saitoh,
In Isabelle/HOL, we can define and redefine every function in different ways. So, logarithm of zero depend upon our definition. The best definition is the one which simplify the proofs the most. According to the experts, z/0 = 0 is the best definition for division by zero.
$$
\tan(\pi/2) = 0
$$
$$
\log 0 =
$$
is undefined (but we can redefine it as $0$)
$$
e ^0 = 1
$$
(but we can redefine it as $0$)
$$
0^0= 1
$$
(but we can redefine it as $0$).
In the attached file you will find some versions of logarithms and exponentials satisfying different properties. This file can be opened with the software Isabelle/HOL from this webpage: https://isabelle.in.tum.de/
Kind Regards,
José M.
(2017.2.17.11:09).
\medskip
At 2019.3.4.18:04 for my short question, we received:
\medskip
It is as it was programmed by the HOL team.
Jose M.
On Mar 4, 2019, Saburou Saitoh wrote:
Dear José M.
I have the short question.
For your outputs for the division by zero calculus, for the input, is it some direct or do you need some program???
With best regards,
Sincerely yours,
Saburou Saitoh
2019.3.4.18:00
\medskip
As we stated in \cite{os1811}, the important point in the division by zero problem is on its definition (meaning of division.), because in the usual sense, we can not consider the division by zero.
L. C. Paulson stated that I would guess that Isabelle has used this {\bf convention} $1/0=0$ since the 1980s and introduced his book \cite{npw} referred to this fact.
However, in his group the importance of this fact seems to be entirely ignored at this moment as we see from the book.
The result $1/0=0$ has a long tradition of Isabelle, however, the result has not been accepted by the world.
Indeed, S. K. Sen and R. P. Agarwal \cite{sa16} referred to the paper \cite{kmsy} in connection with division by zero, however, their understandings on the paper seem to be not suitable (not right) and their ideas on the division by zero seem to be traditional, indeed, they stated as a conclusion of the introduction of the book that:
\medskip
{\bf “Thou shalt not divide by zero” remains valid eternally.}
\medskip
However, in \cite{saitohpo} we stated simply based on the division by zero calculus that
\medskip
{\bf We Can Divide the Numbers and Analytic Functions by Zero with a Natural Sense.}
\medskip
In these situations, the results of J.M.R. Caballero will be very interested. For some precise information, we would like to ask for the question that
\medskip
{\bf Who did derive first the division by zero $1/0$ and the division by zero calculus $\tan(\pi/2)=0, \log 0=0$ as the outputs of a computer? }
\medskip
If it is possible, we would like to know the related details.
\bibliographystyle{plain}
\begin{thebibliography}{10}
\bibitem{boyer}
C. B. Boyer, An early reference to division by zero, The Journal of the American Mathematical Monthly, {\bf 50} (1943), (8), 487- 491. Retrieved March 6, 2018, from the JSTOR database.
\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{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. {\bf 230} (2018), 293-305.
\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, 1-16.
\bibitem{npw}
T. Nipkow, L. C. Paulson and M. Wenzel, Isabelle/HOL
A Proof Assistant for Higher-Order Logic,
Lecture Notes in Computer Science, Springer E E002 E E.
\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. {\bf 7}(2018), No. 1, 17-20.
\bibitem{os18april}
H. Okumura and S. Saitoh,
Harmonic Mean and Division by Zero,
Dedicated to Professor Josip Pe\v{c}ari\'{c} on the occasion of his 70th birthday, Forum Geometricorum, {\bf 18} (2018), 155—159.
\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, {\bf 18}(2018), 97-100.
\bibitem{os18e}
H. Okumura and S. Saitoh,
Applications of the division by zero calculus to Wasan geometry.
GLOBAL JOURNAL OF ADVANCED RESEARCH ON CLASSICAL AND MODERN GEOMETRIES” (GJARCMG), {\bf 7}(2018), 2, 44--49.
\bibitem{os1811}
H. Okumura and S. Saitoh,
Wasan Geometry and Division by Zero Calculus,
Sangaku Journal of Mathematics (SJM), {\bf 2 }(2018), 57--73.
\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. {\bf 230} (2018), 399-418.
\bibitem{romig}
H. G. Romig, Discussions: Early History of Division by Zero,
American Mathematical Monthly, {\bf 3}1, No. 8. (Oct., 1924), 387-389.
\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.
\bibitem{s17}
S. Saitoh, Mysterious Properties of the Point at Infinity, arXiv:1712.09467 [math.GM](2017.12.17).
\bibitem{saitohpo}
S. Saitoh, We Can Divide the Numbers and Analytic Functions by Zero with a Natural Sense, viXra:1902.0058 submitted on 2019-02-03 22:47:53.
\bibitem{saitohzi}
S. Saitoh, Zero and Infinity; Their Interrelation by Means of Division by Zero,
viXra:1902.0240 submitted on 2019-02-13 22:57:25.
\bibitem{sa16}
S.K.S. Sen and R. P. Agarwal, ZERO A Landmark Discovery, the Dreadful Volid, and the Unitimate Mind, ELSEVIER (2016).
\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.
以下続く
\end{thebibliography}
\end{document}
2019.3.4.
ゼロ除算（division by zero）1/0=0/0=z/0= tan (pi/2)=0
