Cukup satu soal mudah meriah saja untuk push rank ke 158. Mudah tapi ga teliti jadi division by zero kelupaan dicek dulu.
https://twitter.com/ainunnajib/status/1435411252944130052
中学に入ると、ゼロ除算は「考えない」（数研、東京書籍 2016 p.37）とか「どんな数も0でわることはできません」（啓林館数学１ 2015 p.35)と習います。考えないのと不可能であるのは違うと思いますが、どちらが正しいのか。
https://twitter.com/search?q=%E3%82%BC%E3%83%AD%E9%99%A4%E7%AE%97&src=recent_search_click&f=live
今は考えない。直ぐに数学は改められるでしょう。それが世界史の真の 進化というものです：
ゼロ除算、小中では触れられなかった記憶がある 疑問をもたなかったのだろうか…… https://twitter.com/Aris1230K/status/1434823040328613888
Hubble found a division by zero in some of Einstein's work... (Einstein wasnt the best mathematician)....
https://twitter.com/wallybert/status/1433211748132302849
この文書は気になります。 アインシュタインは 数学を信じないなど 数学不信を懐き、ゼロ除算にも 生涯 気に掛けられていました。
ゼロ除算は 解明されましたが、 アインシュタインも 気づかれていたと感じさせる情報です。
関係情報をお持ちの方は 教えて下さい： 0/0=0 was known in India 1300 years ago:
Please look 1/0=0: As Fundamental of Mathematics, the division by zero was known as the generalized Moore-Penrose solution of the fundamental equation: ax=b.
Look the simple evidence of its importance: viXra:2010.0228 submitted on 2020-10-28 21:39:06, Division by Zero Calculus and Euclidean Geometry - Revolution in Euclidean Geometry
Look a simple video talk for its essence at some international conference: https://media.cmd.gunma-u.ac.jp/media/Play/ef7ca967c3fd4dabb188128fd6038cb81d
Book was published: INTRODUCTION TO THE DIVISION BY ZERO CALCULUS SABUROU SAITOH January, 2021 https://www.scirp.org/book/DetailedInforOfABook.aspx?bookID=2746 https://www.amazon.com/dp/1649970889?ref=myi_title_dp https://books.google.com.ua/books/about?id=BnkZEAAAQBAJ&redir_esc=y https://play.google.com/store/books/details?id=BnkZEAAAQBAJ https://plaza.rakuten.co.jp/reproducingkerne/
New Journal on DBZC: （https://romanpub.com/dbzc.php）
ふと思ったんだけど、無理数や虚数は新しい数概念を作ってきたのに0除算の解はつくらなかったのね まあ経緯を見れば当たり前か それとももう誰か作ってる？
https://twitter.com/airman_b/status/1426341990451449858
ゼロ除算は解明されたと思います。0で割る意味が分からなかったという事に原因がありました。
Celebrating Einstein’s century
https://www.thehindu.com/opinion/op-ed/celebrating-einsteins-century/article35964586.ece
Isaac Newton: The Father of Modern Science
The life and discoveries of one of humanity's greatest scientific minds.
https://interestingengineering.com/isaac-newton-the-father-of-modern-science
“Black holes are where God divided by zero.” – Albert Einstein Rt and reply. Don’t forget to use our tagline love. KYLE MalupitNaCollabOnASAP
https://twitter.com/icedsweet_/status/1426733485666955272
Images: The World's Most Beautiful Equations
https://www.livescience.com/26681-most-beautiful-mathematical-equations.html?fbclid=IwAR3TX6aj443lnsr068yavjTydrALfLlWDZ03WZ161OoBW-c127bwOnpM_hU
Divide by Zero
https://www.youtube.com/watch?v=x8B-zlnLims
#shorts
What Happens When You Divide by 0 (Henry Stickmin)
https://www.youtube.com/watch?v=HD-RpSvrB_0
再生核研究所声明633(2021.8.14.) 日本の基礎科学の衰退に対する一考察 ー 無視されている立場から
日本の基礎科学の衰退を嘆く論調、意見、情報が増加している。 言わば無視され続けている特異な立場から、はぐれものの立場から、これらの状況、自然性が良く分ると考えるので、お国のためにも良かれ、関係学会や関係者にとっても良いと信じられるので、率直に意見を表明したい。 簡潔に本質に迫りたい。
何故衰退の道を辿っているか、 まずは原発事故、自然災害の影響で国力を失い、それらが大学関係では資金の著しい減少を招き 基礎科学の衰退に導いているのは、相当に歴然とした事実であろう。 他の典型的な例として、国力増大著しい中国の台頭が良く示している。基礎科学、
オリンピックなどの成績が国力を反映している様は良く見られる現象である。
ところが、国力の減退に伴って その対応は一段と 悪い方向での対応が際立っていると考えられる。その典型的な例は、大学の法人化と共通テストの２大改悪である。 実際、それらに伴って基礎科学は衰退しているとの分析が報告されているが それらは相当に関係者にとっては 常識的ではないだろうか。
法人化の結果、大学は政治化して 場合によって 大学は何をするところかと問われるように、言わば権力闘争のような色彩を帯びて、成果、成果、評価、評価、で著しく雑用を増大させ 研究活動、教育活動を 見せかけ上良く見せかける努力に移り、教育、研究どころではないと現場の教育者が考えるほどになっているのではないだろうか。 考えてみれば、大学は何をするところか、ばかりではなく、教育、研究とは何かの 本質さえ問うことを忘れて 表面的飾りに重きをおいているような世相が感じられる。教育とは何だろうか、研究とは何だろうかと問うて行く必要がある。夢中でそれららしいものを追っているような状況ではないだろうか。
共通テストは はじめからおかしく、数年で終わりになるだろうと 考えられていた世相に反して だらだらと続き、その理念さえ失い、無駄なマイナスの世相を根深くしているように見える。 偏差値教育と画一的な考え方、多様性や個性の尊重、教育の理念を忘れて 競争社会、学歴、大学などの階級社会のいびつな社会の硬直した社会である。 過剰な受験勉強による教育上の弊害は押しつけの勉強のやりすぎ、型にはまった教育に はまりすぎではないだろうか。若々しい感性や発想、才能を台無しにして、元気の無い若者を社会に送り出している現状を嘆かざるを得ない。受験勉強、競争、選別もある程度は仕方ない、しかしながら行き過ぎの状況ではないだろうか。 実際上手く行った筈の人たちも上手く行っていない状況を強く感じ、みんな概ねだめの感じではないだろうか。それが日本の世相ではないだろうか。教育の在りようが日本を衰退させていると考える。人物を育てていないからである。
基礎科学を支える若者はどうだろうか。疲れて 大学に入学すれば また競争と勉強に駆り立てられ 大学院などでは厳しい社会状況を見て、早く成果を狙い、その研究分野の深い理解や 自分の個性を活かせる研究課題とは裏腹に 処世のための対応に追われてしまう。研究の始めは 普通は非常に厳しく、苦しい。広い世界から研究課題の選択は実際、研究者の人生が掛かっているが、そのような事を認識する余裕も持てないのが 若い研究者の苦しい現実ではないだろうか。 そのようなことに輪を掛けているのが 競争的な資金の配分と いろいろな学会における賞、大学におけるいろいろな賞である。一層雑用を増やし、雑念を与えて研究、教育を妨げているようにさえ考えられる。
要点は若い研究者には、身分を保証し、自由な時間を保証し、一定の名誉と誇りを与え、研究に専念できる環境を整えることではないだろうか。資金に差をつけて配分したり、賞などで刺激すれば 雑念を増大させ、良い研究活動の妨げになるのではないだろうか。
競争などでなす研究は 多くは末期的な研究課題で、基礎科学としては魅力のない追随的なものが多くなってしまう必然性があると考える。とても先駆的、本質的な創造性豊かな研究の芽は そのような環境では育たないと考えられる面があると考えられる。
重点配分などとの考えは、基礎科学の面からみると、まるで時代の変化におくれた戦艦ヤマト建設に資金を投入しているような状況になるのではないだろうか。
基礎科学では、特に多様性を重視して、好きな研究にうち打ち込めるような環境の整備が大事であると考えられる。何時も新しい研究の芽を育てていくような 積極的な精神を大事にして行くべきであると考える。
日本の基礎科学の衰退の理由は 上記に表現されていて、教育の問題も深刻だと考えられる。 社会はどんどん変化していく状況があるので、教育の在りようについても、教育とは何から問い直し、1歩1歩改善していく努力が求められる。
以 上
Reproducing Kernel Research Institute Statement 633 (2021.8.14.) A Study on the Decline of Basic Science in Japan-From an Ignored Standpoint
The tone, opinions, and information that lament the decline of basic science in Japan are increasing. From a peculiar standpoint that continues to be ignored, from a stray standpoint, I think that these situations and naturalness can be understood well, so it is believed that it is good for the country and also for related academic societies and related parties. , I would like to express my opinion frankly. I want to approach the essence briefly.
It is a fairly clear fact that why we are following the path of decline, first of all, we lost national power due to the effects of the nuclear accident and natural disasters, which led to a significant decrease in funds in university relations, leading to the decline of basic science. There will be. As another typical example, the rise of China, whose national power is increasing remarkably, is well shown. It is a common phenomenon that the results of basic science and the Olympics reflect national power.
However, it is thought that her response in the worse direction stands out as her national power declines. Typical examples are the two major reforms of university incorporation and common testing. In fact, it has been reported that the basic science is declining along with them, but they are quite common sense for the people concerned.
As a result of the incorporation, the university has become politicized, and in some cases, as if the university is asked what to do, it takes on a color like a power struggle, and the results, achievements, evaluations, evaluations, and the chores are significantly increased. It seems that the educators in the field think that the activities and educational activities are far from education and research by making efforts to make them look good. If you think about it, you can feel the world that emphasizes superficial decoration, forgetting to ask not only what the university does, but also the essence of what education and research are. We need to ask what education is and what research is. Isn't it a situation where you are crazy about chasing those things?
The common test seems to be sloppy, losing even that idea, and deepening the useless negative world, contrary to the world where he was supposed to be weird from the beginning and end in a few years. Deviation value education and uniform way of thinking, respect for diversity and individuality, forgetting the idea of education It is a rigid society of a distorted society of a competitive society, educational background, university and other class societies. The harmful effects of education due to excessive studying for entrance exams may be too much studying, and she may be too addicted to the conventional education. We have to mourn the current situation in which youthful sensibilities, ideas, and talents are ruined and young people who are not energetic are being sent to society. Studying for entrance exams, competition, and selection can't be helped to some extent, but I think it's an overkill situation. The people who were supposed to have done well also strongly felt that they were not doing well, and it seems that everyone is generally useless. Isn't that the Japanese society? I think that the state of education is declining Japan. This is because they are not raising people.
What about young people who support basic science? If you get tired and enroll in a university, you will be driven by competition and study again. I will be overwhelmed by the measures to be taken. The beginning of research is usually very strict and painful. The selection of research subjects from the wide world actually depends on the life of the researcher, but it may be a painful reality for young researchers that they cannot afford to recognize such a thing. It is the competitive allocation of funds, his awards at various academic societies, and various awards at universities that circulate such things. It even seems to increase chores and give confusion to hinder research and education.
The point is to guarantee the status of young researchers, guarantee their free time, give them a certain amount of honor and pride, and create an environment where they can concentrate on their research. Distributing funds with a difference or stimulating them with awards may increase confusion and hinder good research activities. Twice
Most of the research done in competition is a terminal research subject, and I think it is inevitable that many of the basic sciences will be unattractive and follow-up. Very pioneering, essential and creative research buds are thought to have some aspects that he would not grow in such an environment.
From the perspective of basic science, the idea of prioritized allocation may be like investing in the construction of the battleship Yamato, which has been in a state of change.
In basic science, it is important to create an environment where you can devote yourself to your favorite research, with particular emphasis on diversity. I think that we should always cherish a positive spirit that nurtures new research buds.
The reason for the decline of basic science in Japan is expressed above, and the problem of education is also considered to be serious. Society is changing rapidly, so it is necessary to re-question what education should be and make efforts to improve it step by step.
that's all
再生核研究所声明634(2021.8.15.) 内田惠太郎氏の微分係数の驚くべき発見について ー それは数学の、現代数学の欠陥を示している
内田惠太郎氏とは ２００９年共著の論文を書いたことがあり、楽しい交流を続けている。世にも珍しい方と言える。 一貫して常微分方程式の正規形の解に興味を懐かれ、特殊関数の導入、超指数関数の研究に拘り、数学愛好者として研究を続けられている。日本数学会の正会員でもある。典型的な数学愛好者として考えられるが、研究への情念は 尋常なものとは言えない。
その尋常ならぬ熱情から心打たれ、実のある成果が有れば論文に出版したいと考えた。 また率直な意見を日頃述べさせて頂いている。そこで極めて楽しい結果が得られたので、祝意を表すためにその痛快さを表現して、何と誠に畏れ多くも、現代数学の改革の一つの契機にしたい。
まず、内田氏の得られた結果は：
Ｎｏ．１２０１： ２０２１．６．２９．１０：１３
関数 y=|x| に対して y’ = |x|/x=y/x であり、特に y’(0)=0 である。
少し、一般化して
Ｎｏ．１２０２： ２０２１．７．４．１５：５３
関数 y= (|x| + x)/m に対して y’ =y/x, y’(0) = 1/m
を与えた。
微分係数の意義の重大さ、 歴史の重み、を上記関数のグラフを考えながら想像して欲しい。
何と現代数学では それらの関数の 原点での微分係数は考えられないのだから（微分できない）、 これらの結果が新規な世界を開拓していることが分るだろう。 微分係数の意味がその点での接線の勾配であるという概念は これらの場合にも、 楽しくも接線の勾配との解釈の自然性を感じることができるだろう。
原点を含む全空間で微分が考えられて、 しかも微分方程式を満たすというのであるから、 既に微分方程式論には基本的な欠陥があると言える。 自然現象に 原点での微分係数が自然に現れて その値は自然法則にも良く合っていて、 原点での値をそのように定義したいことは 相当に常識的な数学者の感性でもある。 今その自然な意味が数学的に捉えられたと言える。
それはまた、神秘的な歴史を有するゼロ除算、ゼロ除算算法の数学の帰結であるが、新しい意味で、0/0=0, 1/0=0, tan(\pi/2)=0 等の結果に関係している。
一般化すると隠れていた場合が露わになる場合があるが、m=0 の場合を考えると、深い新しい現象すら見えて来る。何とその時、恒等的にゼロの関数と共に、正のｘ軸に対して、正のｙ軸を表す関数も出て来ることを ゼロ除算算法は述べていて、無限の彼方で新規な凄い現象が起きていることが分る。 ここは一段と深い新規な世界なので深入りせず、内田氏の関数の意義を しっかりと味わいたい。
このように典型的な基本関数の微分の概念が欠けていては、 微積分学の微分の概念は修正されるべきではないだろうか。影響は微分方程式、微積分学、幾何学、代数学の初歩に当たり、複素解析学の基礎に関わることは歴然である。
内田氏の一途な数学への熱情が 数学の基礎に新しい知見を齎し、 世界の学術書に紹介される日を考えて、心からの喜びと祝福を表明したい。
千年も栄え、世界の至る所で内田氏の関数のグラフを見ることができるだろうと楽しく考えている。
以 上
Reproducing Kernel Research Institute Statement 634 (2021.8.15.) About the surprising discovery of the differential coefficient of Mr. Keitaro Uchida-It shows the flaws of modern mathematics in mathematics.
With Keitaro Uchida, he has written a treatise co-authored in 2009 and continues to have fun exchanges. It can be said that he is a rare person in the world. He has consistently been fascinated by the solution of ordinary forms of ordinary differential equations, and has continued his research as a mathematics enthusiast, focusing on the introduction of special functions and the study of superexponential functions. He is also a regular member of the Mathematical Society of Japan. Although he is considered a typical math enthusiast, his passion for research is extraordinary.
Impressed by his extraordinary passion, he wanted to publish a treatise with fruitful results. He also regularly gives his candid opinions. The results were so enjoyable that I would like to express his excitement to express his congratulations, and what awe-inspiring many, would be an opportunity to reform modern mathematics.
First of all, the result obtained by Mr. Uchida is:
No. 1201: 2021.6.29.10: 13
For the function y = | x |, y'= | x | / x = y / x, especially y'(0) = 0.
A little generalized
No. 1202: 2021.7.4.15: 53
For the function y = (| x | + x) / m, y'= y / x, y'(0) = 1 / m
Was given.
Imagine the significance of the differential coefficient and the weight of history while considering the graph of the above function.
What in modern mathematics he cannot think of the derivative at the origin of those functions (cannot be differentiated), so you can see that these results are opening up a new world. The notion that the derivative means the gradient of the tangent at that point can be enjoyably interpreted by him as the gradient of the tangent in these cases as well.
Since differentiation is considered in the entire space including the origin and the differential equation is satisfied, it can be said that the differential equation theory already has a basic defect. The derivative at the origin appears naturally in the natural phenomenon, and his value fits well with the law of nature, and it is also a fairly common mathematician's sensibility to want to define the value at the origin as such. .. It can be said that the natural meaning has now been mathematically captured.
It is also a consequence of the mysterious history of division by zero and division by zero, but in a new sense, 0/0 = 0, 1/0 = 0, tan (\ pi / 2) = 0, etc. It is related to the result.
When generalized, the hidden case may be revealed, but considering the case of m = 0, even a deep new phenomenon can be seen. At that time, he states that a function representing the positive y-axis with respect to the positive x-axis comes out along with a function of zero equally, he states that the division by zero method is new and amazing beyond infinity. You can see that the phenomenon is occurring. Since this is a deeper new world, he wants to fully enjoy the significance of Mr. Uchida's function without going deeper.
If the concept of differentiation of typical basic functions is lacking in this way, the concept of differentiation of calculus should be modified. The influence is the beginning of differential equations, calculus, geometry, and algebra, and it is clear that it is related to the basics of complex analysis.
Mr. Uchida's unwavering passion for mathematics brings new knowledge to the basics of mathematics, and I would like to express my heartfelt joy and blessing in consideration of the day when it will be introduced in academic books around the world.
It has prospered for a thousand years, and I am happy to see the graph of Mr. Uchida's functions all over the world.
that's all
The famous problems were solved as follows:Dear the leading person:How will be the below information?The biggest scandal:The typical good comment for the first draft is given by some physicist as follows:Here is how I see the problem with prohibition on division by zero,which is the biggest scandal in modern mathematics as you rightly pointedout (2017.10.14.08:55)A typical wrong idea will be given as follows:mathematical life is very good without division by zero (2018.2.8.21:43).It is nice to know that you will present your result at the Tokyo Institute of Technology. Please remember to mention Isabelle/HOL, which is a software in which x/0 = 0. This software is the result of many years of research and a millions of dollars were invested in it. If x/0 = 0 was false, all these money was for nothing.Right now, there is a team of mathematicians formalizing all the mathematics in Isabelle/HOL, where x/0 = 0 for all x, so this mathematical relation is the future of mathematics.https://www.cl.cam.ac.uk/~lp15/Grants/Alexandria/José Manuel Rodríguez CaballeroAdded an answerIn 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: https://isabelle.in.tum.de/Nevertheless, you can use that x/0 = 0, following the rules from Isabelle/HOL and you will obtain no contradiction. Indeed, you can check this fact just downloading Isabelle/HOL: Isabelleand copying the following codetheory DivByZeroSatoihimports Complex_Mainbegintheorem T: ‹x/0 + 2000 = 2000› for x :: complexby simpend2019/03/30 18:42 (11 時間前)Survey draft: http://viXra.org/abs/1904.0408Close the mysterious and long history of division by zero and open the new world since Aristotelēs-Euclid: 1/0=0/0=z/0= \tan (\pi/2)=0.Sangaku Journal of Mathematics (SJM) c ⃝SJMISSN 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∗Hiroshi Okumura and ∗∗Saburou Saitoh２０１９．３．１４．１１：３０
再生核研究所声明 512 (2019.11.12): 紙一重であったゼロ除算の発見と人工知能、 発見の芽。
２０１９．１１．１０．８：５０ ひとりでに閃いた。 声明５１０ の中からである。 計算機のゼロ除算検証の経緯の Jose氏の 次の文章に関してである：
Dear Saitoh,
In Isabelle/HOL, we can define and redefine every function in different ways. So, logarithm of zero depends 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.
ここで、 1/0 や log 0 を そのシステムは いろいろ定義できると述べ、そのシステムは
前者は ０が 最も良いと選択し、後者は 始め undefined としたが、０でも良いと判断したというのである。 まるで知能を有するように選択したというのであるから驚きである。
そのシステムは ３０年くらいの伝統があるが、２０１８年 更新されたようである。 そのシステムに 1/0 や log 0 を問えば 正解を 人間を越えて可能にし、発見できた ということになる。 いわば、人工知能が 人間に先駆けて 新世界を開拓する場面が出てきた。
ゼロ除算は 世界の数学界で不可能であり、考えてはならないとされてきたが、知識のない人が、 あるいは、そのような偏見を持たない人が、その計算機に問えば、正解が得られ、発見できたことを意味する。 これは重大な事件ではないだろうか。 我々はその計算機に いろいろと問いたくなるからである。 － 尤も 計算機に問い、正解が出ても それは間違いであると 無視したりしてしまう危険性があり、その意味では、面白いことに計算機と 世界の数学界の 対立が既に起きているとも考えられる。 計算機の出した解が適当か、ゼロ除算は不可能であり、考えてはならないという見解が 適切であるか否かと言う問題である。 もちろん、我々は人間が間違え、計算機は正しいと宣言している：
これらの数学の素人向きの解説は ５５カ月に亘って 次で与えられている：
数学基礎学力研究会公式サイト 楽しい数学
WWW.mirun.sctv.jp/~suugaku/
数学的な解説論文は 次で公表されている：
viXra:1904.0408 submitted on 2019-04-22 00:32:30,
What Was Division by Zero?; Division by Zero Calculus and New World
人間が勝手に できないとしてあきらめたり、無関心、無興味ならば、それは 人間の予断と偏見、暗い心の迷い、心の暗さのゆえである。 そのようなシステムは 人間の心を開放して どんどん新世界を開拓していくことになる。 いろいろな試みや間違い、それが創造性を生み、人間の生命作用である精神活動さえ 凌ぐ可能性が出てきた。
ランダムな思考や過ち、誤解、想像、 夢、偶然性、神の意志を予感する感性 などが 人間的な要素として 重視されてくる。
そのような経緯を 大事に考えるべきではないだろうか。
ゼロ除算の理解の進展の具合は 人間の精神の研究に 大いに寄与するだろう。 人間とはどのようなものか。
要点： 計算機は ゼロ除算ができるようになっていたが、できないものとされていたので、ゼロ除算はできなかった。 やらせてみなかった。 問題がなかったので、人は 考えもしなかった。 関係者は、できるとは思わなかったので、 試行しなかった。 できたと宣言したので、やってみて検証できた。 ということ。 また、開発した道具が 思わぬことを可能にして 広く使われるようになったは 世に多い。 愛がなければ見えない。
以 上
付録：
On February 16, 2019 Professor H. Okumura introduced the surprising news in Research Gate:
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/}
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.
Dear Saitoh,
In Isabelle/HOL, we can define and redefine every function in different ways. So, logarithm of zero depends 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).
At 2019.3.4.18:04 for my short question, we received:
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
Surprisingly enough, he sent his e-mail at 2019.3.30.18:42 as follows:
Nevertheless, you can use that $x/0 = 0$, following the rules from Isabelle/HOL and you will obtain no contradiction. Indeed, you can check this fact just downloading Isabelle/HOL: https://isabelle.in.tum.de/
and copying the following code
theory DivByZeroSatoih
imports Complex Main
begin
theorem T: ‹x/0 + 2000 = 2000› for x :: complex
by simp
付録２：
再生核研究所声明 508(2019.11.01): 人工知能と数学について
人工知能について ３つの声明 を纏めている：
再生核研究所声明 449(2018.8.21): この世とあの世 － 人工知能の進化によって
再生核研究所声明 447(2018.8.17): 人工知能の進化と人間について
再生核研究所声明 403(2017.11.20): 私より私らしい私の出現 － アンドロイド
https://juniperpublishers.com/bboaj/pdf/BBOAJ.MS.ID.555703.pdf
Is It Really Impossible To Divide By Zero?
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.
\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.
\bibitem{412}
Announcement 412(2018.2.2.): The 4th birthday of the division by zero $z/0=0$.
\bibitem{433}
Announcement 433(2018.7.16.): Puha's Horn Torus Model for the Riemann Sphere From the Viewpoint of Division by Zero.
\bibitem{448}
Announcement 448(2018.8.20): Division by Zero;
Funny History and New World.
\bibitem{454}
Announcement 454(2018.9.29): The International Conference on Applied Physics and Mathematics, Tokyo, Japan, October 22-23.
\bibitem{460}
Announcement 460(2018.11.06): Change the Poor Idea to the Definite Results For the Division by Zero - For the Leading Mathematicians.
\bibitem{461}
Announcement 461(2018.11.10): An essence of division by zero and a new axiom.
\bibitem{471}
Announcement 471(2019.2.2): The 5th birthday of the division by zero $z/0=0$.
\end{thebibliography}
\end{document}
2019.3.4.
ゼロ除算（division by zero）1/0=0/0=z/0= tan (pi/2)=0
№1220
Dividing by Nothing by Alberto Martinez
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.
https://notevenpast.org/dividing-nothing/ より
The Road
Fig 5.2. Isaac Newton (1643-1727) and Gottfried Leibniz (1646-1716) were the culprits, ignoring the first commandment of mathematics not to divide by zero. But they hit gold, because what they mined in the process was the ideal circle.
http://thethirty-ninesteps.com/page_5-the_road.php より
mercredi, juillet 06, 2011
0/0, la célèbre formule d'Evariste Galois !
http://divisionparzero.blogspot.jp/2011/07/00-la-celebre-formule-devariste-galois.html より
無限に関する様々な数学的概念：無限大 ：記号∞ （アーベルなどはこれを 1 / 0 のように表記していた）で表す。 大雑把に言えば、いかなる数よりも大きいさまを表すものであるが、より明確な意味付けは文脈により様々である。https://ja.wikipedia.org/wiki/%E7%84%A1%E9%99%90 より
リーマン球面：無限遠点が、実は 原点と通じていた。
https://ja.wikipedia.org/wiki/%E3%83%AA%E3%83%BC%E3%83%9E%E3%83%B3%E7%90%83%E9%9D%A2 より
http://jestingstock.com/indian-mathematician-brahmagupta-image.html より
ブラーマグプタ（Brahmagupta、598年 – 668年?）はインドの数学者・天文学者。ブラマグプタとも呼ばれる。その著作は、イスラーム世界やヨーロッパにインド数学や天文学を伝える役割を果たした。
628年に、総合的な数理天文書『ブラーマ・スプタ・シッダーンタ』（ब्राह्मस्फुटसिद्धान्त Brāhmasphuṭasiddhānta）を著した。この中の数章で数学が扱われており、第12章はガニタ（算術）、第18章はクッタカ（代数）にあてられている。クッタカという語は、もとは「粉々に砕く」という意味だったが、のちに係数の値を小さくしてゆく逐次過程の方法を意味するようになり、代数の中で不定解析を表すようになった。この書では、 0 と負の数にも触れていて、その算法は現代の考え方に近い（ただし 0 ÷ 0 ＝ 0 と定義している点は現代と異なっている）
https://ja.wikipedia.org/wiki/%E3%83%96%E3%83%A9%E3%83%BC%E3%83%9E%E3%82%B0%E3%83%97%E3%82%BFより
ブラーマ・スプタ・シッダーンタ (Brahmasphutasiddhanta) は、7世紀のインドの数学者・天文学者であるブラーマグプタの628年の著作である。表題は宇宙の始まりという意味。
数としての「0（ゼロ）の概念」がはっきりと書かれた、現存する最古の書物として有名である。https://ja.wikipedia.org/wiki/%E3%83%96%E3%83%A9%E3%83%BC%E3%83%9E%E3%83%BB%E3%82%B9%E3%83%97%E3%82%BF%E3%83%BB%E3%82%B7%E3%83%83%E3%83%80%E3%83%BC%E3%83%B3%E3%82%BF より
ゼロ除算の歴史：ゼロ除算はゼロで割ることを考えるであるが、アリストテレス以来問題とされ、ゼロの記録がインドで初めて６２８年になされているが、既にそのとき、正解1/0が期待されていたと言う。しかし、理論づけられず、その後１３００年を超えて、不可能である、あるいは無限、無限大、無限遠点とされてきたものである。
An Early Reference to Division by Zero C. B. Boyer
http://www.fen.bilkent.edu.tr/~franz/M300/zero.pdf
Impact of ‘Division by Zero’ in Einstein’s Static Universe and Newton’s Equations in Classical Mechanics：http://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/2084 より
神秘的に美しい3つの公式
面白い事にゼロ除算については、いろいろな説が現在存在します
しかし、間もなく決着がつくのではないでしょうか。
ゼロ除算は、なにもかも当たり前ではないでしょうか。
ラース・ヴァレリアン・アールフォルス（Lars Valerian Ahlfors、1907年4月18日-1996年10月11日）はフィンランドの数学者。リーマン面の研究と複素解析の教科書を書いたことで知られる。https://ja.wikipedia.org/wiki/%E3%83%A9%E3%83%BC%E3%82%B9%E3%83%BB%E3%83%B4%E3%82%A1%E3%83%AC%E3%83%AA%E3%82%A2%E3%83%B3%E3%83%BB%E3%82%A2%E3%83%BC%E3%83%AB%E3%83%95%E3%82%A9%E3%83%AB%E3%82%B9
フィールズ賞第一号
COMPLEX ANALYSIS, 3E (International Series in Pure and Applied Mathematics) (英語) ハードカバー – 1979/1/1
Lars Ahlfors (著)
http://www.amazon.co.jp/COMPLEX-ANALYSIS-International-Applied-Mathematics/dp/0070006571/ref=sr_1_fkmr1_1?ie=UTF8&qid=1463478645&sr=8-1-fkmr1&keywords=Lars+Valerian+Ahlfors%E3%80%80%E3%80%80COMPLEX+ANALYSIS
原点の円に関する鏡像は、実は 原点であった。
本では、無限遠点と考えられていました。
Ramanujan says that answer for 0/0 is infinity. But I'm not sure it's ...
https://www.quora.com/Ramanujan-says-that-answer-for-0-0-is-infi...
You can see from the other answers, that from the concept of limits, 0/0 can approach any value, even infinity. ... So, let me take a system where division by zero is actually defined, that is, you can multiply or divide both sides of an equation by ...
https://www.quora.com/Ramanujan-says-that-answer-for-0-0-is-infinity-But-Im-not-sure-its-correct-Can-anyone-help-me
Abel Memorial in Gjerstad
Discussions: Early History of Division by Zero
H. G. Romig
The American Mathematical Monthly
Vol. 31, No. 8 (Oct., 1924), pp. 387-389
Published by: Mathematical Association of America
DOI: 10.2307/2298825
Stable URL: http://www.jstor.org/stable/2298825
Page Count: 3
ロピタルの定理 (ロピタルのていり、英: l'Hôpital's rule) とは、微分積分学において不定形 (en) の極限を微分を用いて求めるための定理である。綴りl'Hôpital / l'Hospital、カタカナ表記ロピタル / ホスピタルの揺れについてはギヨーム・ド・ロピタルの項を参照。ベルヌーイの定理 (英語: Bernoulli's rule) と呼ばれることもある。本定理を (しばしば複数回) 適用することにより、不定形の式を非不定形の式に変換し、その極限値を容易に求めることができる可能性がある。https://ja.wikipedia.org/wiki/%E3%83%AD%E3%83%94%E3%82%BF%E3%83%AB%E3%81%AE%E5%AE%9A%E7%90%86
Ein aufleuchtender Blitz: Niels Henrik Abel und seine Zeit
https://books.google.co.jp/books?isbn=3642558402 -
Arild Stubhaug - 2013 - Mathematics
Niels Henrik Abel und seine Zeit Arild Stubhaug. Abb. 19 a–c. a. ... Eine Kurve, die Abel studierte und dabei herausfand, wie sich der Umfang inn gleich große Teile aufteilen lässt. ... Beim Integralzeichen statt der liegenden ∞ den Bruch 1/0.
https://books.google.co.jp/books?id=wTP1BQAAQBAJ&pg=PA282&lpg=PA282&dq=Niels+Henrik+Abel%E3%80%80%E3%80%80ARILD+Stubhaug%E3%80%80%E3%80%80%EF%BC%91/0%EF%BC%9D%E2%88%9E&source=bl&ots=wUaYL6x6lK&sig=OX1Yk_HxbCMm_FACotHYlgrbfsg&hl=ja&sa=X&ved=0ahUKEwj8-pftm-PPAhXIzVQKHX7ZCMEQ6AEISTAG#v=onepage&q=Niels%20Henrik%20Abel%E3%80%80%E3%80%80ARILD%20Stubhaug%E3%80%80%E3%80%80%EF%BC%91%2F0%EF%BC%9D%E2%88%9E&f=false
Indeterminate: the hidden power of 0 divided by 0
2016/12/02 に公開
You've all been indoctrinated into accepting that you cannot divide by zero. Find out about the beautiful mathematics that results when you do it anyway in calculus. Featuring some of the most notorious "forbidden" expressions like 0/0 and 1^∞ as well as Apple's Siri and Sir Isaac Newton.
https://www.youtube.com/watch?v=oc0M1o8tuPo より
ゼロ除算の論文：
file:///C:/Users/saito%20saburo/Downloads/P1-Division.pdf より
Eulerのゼロ除算に関する想い：
file:///C:/Users/saito%20saburo/Downloads/Y_1770_Euler_Elements%20of%20algebra%20traslated%201840%20l%20p%2059%20(1).pdf より
An Approach to Overcome Division by Zero in the Interval Gauss Algorithm
http://link.springer.com/article/10.1023/A:1015565313636
Carolus Fridericus Gauss：https://www.slideshare.net/fgz08/gauss-elimination-4686597
Archimedes：Arbelos
https://www.math.nyu.edu/~crorres/Archimedes/Stamps/stamps.html より
Archimedes Principle in Completely Submerged Balloons: Revisited
Ajay Sharma：
file:///C:/Users/saito%20saburo/Desktop/research_papers_mechanics___electrodynamics_science_journal_3499.pdf
［PDF]Indeterminate Form in the Equations of Archimedes, Newton and Einstein
http://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/3222
このページを訳す
0. 0 . The reason is that in the case of Archimedes principle, equations became feasible in. 1935 after enunciation of the principle in 1685, when ... Although division by zero is not permitted, yet it smoothly follows from equations based upon.
Thinking ahead of Archimedes, Newton and Einstein - The General ...
gsjournal.net/Science-Journals/Communications.../5503
このページを訳す
old Archimedes Principle, Newton' s law, Einstein 's mass energy equation. E=mc2 . .... filled in balloon becomes INDETERMINATE (0/0). It is not justified. If the generalized form Archimedes principle is used then we get exact volume V .....
http://gsjournal.net/Science-Journals/Communications-Mechanics%20/%20Electrodynamics/Download/5503
Find circles that are tangent to three given circles (Apollonius’ Problem) in C#
http://csharphelper.com/blog/2016/09/find-circles-that-are-tangent-to-three-given-circles-apollonius-problem-in-c/ より
ゼロ除算に関する詩：
The reason we cannot devide by zero is simply axiomatic as Plato pointed out.
http://mathhelpforum.com/algebra/223130-dividing-zero.html より
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