A new publication clearly proving that Takayama Masayuki is the only journalist in the postwar world is a must read for Japanese citizens and people all over the world.

I am in a book review column of the 7/7 Sankei Shimbun, but in the content introduction there was a section of ‘Asahi Shimbun that attacks Toshiba as much as possible’.

For a moment, I could not understand why the Asahi Shimbun was attacking Toshiba so much.

Yesterday, at 7 o’clock news, in Fuchu, Hiroshima, despite being sunny, suddenly the river was flooded.

French satellite pictures were aired that there were many landslides that have not been confirmed yet.

I remembered even my anger.

Asahi Shimbun not only severely hurt Japan’s honor and credibility in comfort women, Nanjing massacre, etc.

As a result, Japan provided the largest financial support for human history to China, and the Communist Party single-party dictatorship Not only is it helping to increase the economy and military capabilities of China and continuing violating acts against Japanese territory,

By switching the power generation of 30 million KW to fossil fuel by the absolute opposition movement against nuclear power plant, we reduced the national wealth of Japan by 15 trillion yen in just a few years.

Because of stopping all nuclear power plants and switching to fossil fuels,

Globally warming gases generated in the sky above Japan caused abnormal weather in the last few years and finally it has destroyed Japan’s land by catastrophe of concentrated torrential rain that covered this western Japan area It is from.

At that time, suddenly I understood.

The reason the Asahi Shimbun attacked Toshiba abnormally on the paper is that Toshiba is one of the companies with the world’s best nuclear technology.

Their movement against nuclear power plants that seems to be manipulation of China and the Korean Peninsula any longer,

In industrial power, military power greatly reduces Japan’s national strength …

Because it is a well-known fact that China and South Korea decide nuclear power plant expansion as the country opposite to Japan.

Anyway, to say Asahi Shimbun is an unusual company.

They attack violently their opponent who opposes their masochistic view of history, anti-Japanese thought, placebo moralism.

It is no longer a decent human group

Many citizens were in sync with their opinion survey on such a newspaper company ‘s opposition to nuclear reactivation movement.

So, the government was still unable to return nuclear power to its original state.

Meanwhile, it continued to burn oil, coal, LPG … fossil fuel emitting greenhouse gas.

In fact, Japan’s global warming since 2011 will be sharp.

Otherwise as in the past ghosts for the first time in 40 years Smog cannot cover Japan.

As I mentioned earlier, the amount of power generated by each nuclear power plant is extremely large.

Three people mentioned as having repeatedly stopped all 54 nuclear power plants that were in the best 3 in the world as well as the media such as the Asahi Shimbun and NHK which has been in tune with this and the opposition party politicians is there.

The decision to immediately stop the main power supply that had been generating power exceeding 30 million kW always was a stupidity less than kindergarten and not policy decisions of decent country.

It is no wonder that the world’s merchants have multiplied their stupidity.

Immediately, they called Japan premium, etc. for fossil fuels for Japan and sold it to Japan with a large profit added.

It would be so. Even if Japan does not buy no matter how expensive it is, the economy will collapse in an instant … because the supply of electricity, which is the minimum requirement for the civilized state, stops and it becomes a dark society.

The national wealth lost by Japan because of such foolishness as such a kindergarten child is 15 trillion yen in just a few years.

Correct the disparity the Asahi Shimbun and the opposition politicians talk about in government attacks and placebo moralism et. Can achieve 100%,

The huge amount of national wealth = taxes disappeared while generating a large amount of greenhouse gas.

I thought that the torrential rain that struck the western part of Japan, which is nothing more than this anomaly,

Three people who alone they are rogues no longer,

And Asahi Shimbun and NHK nuclear power plants promoted by media such as has been in sync with this re-work absolute opposition campaign,

I assert that it is the result they brought.

There is only one thing to argue, what people should be thinking about by unfortunate people suffering from abnormal weather.

If you really care about your hometown until you die, instantly restart the nuclear power plant at once, where you really live now, your living base! … LNG, Coal, Oil Warming Gas Decrease the use of fossil fuels as a source of gas instantly, greatly … to return to the state by 2011!

Besides that, you should know that there is no way for you to live in the present place.

If you abandon your hometown you love, there are a lot of unnecessary people, unusually high residential cost Tokyo … Tokyo where the media such as the Asahi Shimbun and NHK concentrate,

You do not love your hometown so much, you think that you can abandon anytime, like Tokyo … If you want to live in such a city, the story is different,

As it stands, even if nuclear power plants are not allowed to operate again, if we continue to burn greenhouse gas emissions and fossil fuels that are over 30 million kilowatts, life in your hometown will no longer be possible.

Back in the mountains I knew as a child

Fish filled the rivers and rabbits ran wild

Memories, I carry these, wherever I may roam

I hear it calling me, my country home

Mother and Father, how I miss you now

How are my friends I lost touch with somehow?

When the rain falls or the wind blows

I feel so alone

I hear it calling me, my country home

I’ve got a dream and it keeps me away

When it comes true, I’ll go back there someday

Crystal waters, mighty mountains

Shining like an emerald stone

I hear it calling me, my country home,

As it can no longer be a mountain landslide, landslide mountain, flooding, overflow river,

You should notice things that you can only lose your homeland by continuing to agree with the magazine media such as the Asahi Newspaper and NHK and the political shoes of opposition parties and anti-Japanese thought, anti-moralism, zombie communism The time has arrived.

小林由香 「罪人が祈るとき」
小林さんの「ジャッジメント」を読んでから、新しいのが出ないかと気にしていました。

 

　
その町では11月6日に自殺者が出る呪いがあると噂されていた。主人公の少年は酷いいじめを苦に相手を殺して自分も自殺する決意をしていた。ある日公園で出会ったピエロが殺人計画を立ててくれたら計画を手伝うと約束してくれる。
もう一人の主人公の男性は自殺で息子と妻を続けて亡くしていた。息子の死はいじめが原因だと思っていたが学校側と生徒らは一切認めなかった。生きる気力をなくしていたが、息子に何があったかを知っていそうな人物と出会い、再度息子の死の真相を探ろうとする、というお話。
　
「いじめをする人間とされる人間」をテーマに書かれています。世間でも最近いじめによる自殺を報じているため、話題性はありそうです。
本書では学校機関側のことは触れておらず、いじめをする側、される側の心理を中心に書いています。
ミステリーとも書かれていますが、メインは登場人物たちの心理描写です。とても上手くとても上手く表現されており、特に主人公サイドの人たちの心情があまりに痛ましくて読むのが辛い場面もありました。
今のいじめはこれほど陰湿で残酷だと改めて見せられました。昔よりも情報社会になっているため、脅す材料や攻撃する武器を手に入れるのがはるかに簡単になっていることがよく分かります。
　
本書を読んでいると「いじめをする人間に生きている価値がないのでは？」としきりに投げかけてきます。
これを話すと「どんな子供でも未来には可能性が～～～」という論調が出てしまうので、別の視点から私の考えを書きます。
私は「いじめをする人間は殺していい」と思っています。理由はいじめをして自殺に追い込んで殺そうとしてくるのですから、相手を殺して止めるのは当然の権利だと考えているからです。手法は違えどお互いに「殺し」を使って攻撃しあうのですから、受ける側も武装して挑み「戦って負けた方が死ぬ」という対等な状態を作ればいい。
今はアマゾン覗けば斧や鉈は簡単に手に入りますし、お金出せばボウガンや毒薬など強力な武器も手に入るので相手の危機度に合わせて武装すればいいのです。今の日本は大人も子供も暴力に対して対抗する手段を持っていないとすぐストレス発散の標的にされて攻撃されます。通り魔などはもちろん許されませんが、自分に害をなす人間を排除する力は持つべきだと私は思っています。
　
それと「子供には更生の可能性がある」という点についても考えてみました。
根底的な性格の更生を外部からの働きかけで起こせるのは中学生あたりまでだと私は見ています。それより上の年齢になると例えば「長年築いた地位や巨額の富を失う」「大切な人を失う」など自身に甚大なダメージが発生する出来事が起きない限り更生の可能性はほぼ0です。「直さないと大きな損をする」という意識が芽生えない限り起こりえないということです。

 

もし自分の子供がいじめをしていたらどうするか？についてはけっこう前からどうするか決めています。親として責任もって殺処分します。世の中に汚物以下の物体を生み出してしまったのですから責任もって自分で処分しなければなりません。一つ前のように書いておきながら自分の子供は更生してくれる、なんて考えてたらそれこそ愚か者です。

　
この作品はぜひ小さなお子さんをお持ちの方に読んでもらいたい。対策しないと殺されるという意味では日本のいじめはもはやテロと同等かそれ以上の脅威になりつつあるので、どうするか考えるいいきっかけになると思います。
　
　
Yuka Kobayashi “When a sinner prays”
I was waiting for Ms. Kobayashi’s novel to appear since I read “Judgement”.
　
It was rumored in that town that there was a curse that suicide came out on November 6. The hero’s boy was suffering from severe bullying, and he was determined to kill himself after he killed his opponent. One day the clown he met in the park pledges a murder plan will promise to help the plan.
Another male protagonist lost his son and his wife on suicide. He thought that the death of my son was caused by bullying, but the school side and the students did not admit it at all. At one time he met a person who knew what happened to his son. He tries to find out the truth of my son’s death again.
　
This is written about “bullies”. It is likely that there is a topicality because the world reports recently suicide by bullying. She does not mention about school agencies in this, mentions about victims and perpetrators. 
Also written as a mystery, the main is a psychological depiction of the characters. It is very well represented, 
there was also a scene where the heart of people on the main character side was so painful that it was hard to read.  I was seen once again that bullying now is so humid and cruel. Because it is becoming an information society than in the past, we can see that it is much easier to get threatening materials and attacking weapons.
　
She writes about “Is not it worth living to humans who bully?” in this.
There are people who insist on “There is a possibility in the future for any child”, so I will draw an idea from another perspective.
I think “human beings who bully are killed and have no problem”. 
It is comparable that he kills and stops the person who try to kill by driving him to suicide by bullying. The method uses different “kill” mutually, but attacks each other, so we can create an equal condition that “one who fought and loses will die”. Now we can easily get ax and hammer if I peep at the Amazon, and if we put out money we can also obtain powerful weapons such as bow guns and poisons. 
Nowadays Japan is attacked as soon as both adults and children do not have a means to counter violence. I think that we should have the power to eliminate humans who harm ourselves.
　
And I also thought about the point that “children have the possibility of rehabilitation”.
I think that it is up to the junior high school students that I can cause rehabilitation of the fundamental personality with external intervention. The likelihood that people older than that will be rehabilitated is almost 0%. There will not be reorganization unless events such as “Losing the status you have built for many years or losing huge wealth”, “Losing important people” and so on, causing enormous damage to yourself. 

 

 

What should I do if my child is teasing? I am deciding what to do from pretty well.　I will kill it with responsibility as a parent. Since we have created objects below the filth in the world, we must dispose of it on our own with responsibility. It is a fool if you think about how your child will be reborn while you write it as before.

I want people who have small children to read this. Japanese bullying is no less a threat than terrorism in the sense that it is killed unless measures are taken, so I think that it will be a good inspiration to think about what to do.

Thank you for reading!!

Sir Isaac Newton and Judaism

The scientist’s recently disclosed private papers reveal his deep reverence for ancient Jewish wisdom.

---

Sir Isaac Newton was one of the greatest scientists of all time. Some of his most outstanding discoveries include the laws of optics or the physics of light, the three laws of motion, the laws of gravity, and calculus. He is also famous for his Principia Mathematica, the most widely read scientific work of all time, in which he explains the motions of the planets in a single mathematical system. Born in an age that embraced rationalism and shunned religious authority, Newton was also hailed as a hero of his era. Yet, recent divulgement of Newton’s personal writings challenges all common assumptions about his true identity.

Newton’s Private Beliefs

Newton’s private beliefs have been kept under wraps for hundreds of years, probably because of their unfavorable reception. Bernard Cohen’s book Franklin and Newton discusses the first time scientists discovered Newton’s personal manuscripts: He quotes John Maynard Keynes, the British great economist: “‘Upon his death in 1727, a very big box of unusual papers was discovered in his room. Bishop Samuel Horsley, who was also a scientist, was asked to inspect the box with view to publication. He saw the contents with horror and slammed the lid…’ shut.” The recent disclosure of Newton’s private manuscripts revealed that Newton was far from the archetype rationalist he was originally assumed to be.

A page of Isaac Newton’s writing featuring, the prayer, in Hebrew,
‘Blessed is His name for eternity.’

After being tucked away for 200 years,  were finally auctioned off in 1936. Keynes, The Babson family in America, and Israeli Professor Avraham Shalom Yahuda bought the majority of them and donated them to university libraries around the world. These manuscripts have been made available in the past 25 years.

Newton’s “strange” interests

It’s no wonder that both Christian and secular-minded scientists who had originally revered Newton had little incentive to publicize their findings. Newton’s manuscripts revealed that he took a keen interest in “archaic” Jewish wisdom. Newton’s knowledge of Jewish thought was not superficial; he referred to rabbinic works such as the Aramaic Version of Esther, Vayikra Rabba, the commentaries of Sa’adia HaGaon, Ibn Ezra, Rashi, Sifra, R. Aharon ibn Hayyim; Seder Ma’amadot (about the daily sacrifices) the Bartinurah and Talmudic passages from the Babylonian and Jerusalem Talmud in Latin. One of Newton’s manuscripts was entitled “On Maimonides,” where he quoted the Latin translation of Maimonides’ Mishneh Torah. ¹

Sir Isaac Newton

But the content in Newton’s notes should not really have come as such a big surprise, given the collection of works in his library. Newton kept five works of Maimonides essays in his library.² He also owned a Latin commentary on Maimonides that references the Moreh Nevuchim, The Guide to the Perplexed, Maimonides’ reconciliation of Torah with science and philosophy. This particular work seems to have had a significant impact on Newton’s philosophy. The harmony between scripture and science was a theme threaded throughout many of Newton’s works, and a means through which he carried out his theological and scientific pursuits.³

Newton’s beliefs, revealed

Maynard Keynes, the scholar who studied Newton’s manuscripts, summarized his findings in honor of the 300^th anniversary of Newton’s death. Keynes explained that Newton’s beliefs were influenced by Maimonides’ philosophy. Keyne’s described Newton as “a Judaic monotheist of the school of Maimonides”. In fact, in his work The Principia, Newton rejected the concept of the deity for a belief that closely mirrored the Jewish monotheistic concept of God. (Newton even quotes an element in Maimonides’ teachings: that one can only learn about God indirectly, through His actions and His dominion.)⁴

Newton’s theological writings at Israel’s National Library in Jerusalem, October 2014.
(photo credit: AP Photo/Sebastian Scheiner)

Newton’s leanings were not limited to the intellectual sphere, and he appears to have kept the seven commandments of the children of Noah that the Torah has given to non-Jews. To quote, in his own words, in Theological Manuscripts: “Although the precepts of Noah are not as perfect as the religion of the Scripture, they suffice for salvation… Indeed, (as the rabbis taught) Jews had admitted into their gates heathens who accepted Noah’s precepts, but had not converted to the Law of Moses.” Newton professed that commandment against eating “the flesh” or “the blood of (live) animals” is because “this religion obliged men to be merciful even to brute beasts.”⁵

Newton’s Scientific Works and Maimonides

What may have irked scientists more than Newton’s private beliefs and practices was how he applied these beliefs to his theological and scientific studies. Parallels of Newton’s philosophy and Maimonides’ teachings are interwoven in his manuscripts. For example, Newton used Maimonides’ “Laws of Sanctification of the New Moon” in his notes on “considerations about rectifying the Julian calendar”.

Newton studied the measurements of Solomon’s Temple and the Third Temple to come to a greater understanding of the earth’s dimensions. He understood that the Temple was a microcosm of the earth and “revealed the works of God”, the world’s greatest architect.⁶

To that end, Newton quoted excerpts from the Latin translation of Maimonides’ De Cultu Divino, where he explained the measurements of the Temple.⁷ Newton also preoccupied himself with studies on the Jewish cubit or the amah (measurements used to build the Temple, the tabernacle, and its vessels) and the measurements of The Great Pyramid of Giza, which he believed to have derived from the Jewish cubit. He wasn’t merely dabbling in mathematics; the accuracy of his analysis of the circumference of the earth and his theory on gravity were dependent on these findings. He recorded his calculations of the Jewish cubit in his work A Dissertation upon the Sacred Cubit of the Jews and Cubits of the several Nations.”⁸

Many scientists who feel less than favorably toward Newton’s beliefs and his method of study consider him a fool who dabbled in mysticism and pseudoscience. In response to the critics, John Maynard Keynes wrote: “There was extreme method in his madness…All his unpublished works… are marked by careful learning, accurate method, and extreme sobriety of statement, they (his controversial works) were nearly all composed during the same 25 years of his mathematical studies.”⁹

Much of Newton’s private life, as well as some of the drafts of his scientific works, is still hidden from us. It’s perhaps no wonder that he hid his true identity and means of study from the public; he would have likely been ostracized and his scientific discoveries immediately dismissed. Sarah Dry, author of The Newton Papers, notes that gaps in his original draft of The Principia suggests that he deliberately concealed them. Says Dry, “And it’s because Newton didn’t want people to know how he had come to his knowledge. I think that might relate to his religious beliefs.”

Newton’s outstanding discoveries single him out as one of the greatest science influencers of all time. Perhaps we can now add his attempt to reconcile ancient scripture with science as yet another unique, albeit undervalued,
accomplishment of Sir Isaac Newton.

---

1. Newton, Maimonides, and Esoteric Knowledge, Faur Jose, Cross Currents, http://moreshetsepharad.org/media/Newton_Mathematics_and_Esoteric_Knowledge.pdf
2. Essays on the Context, Nature and Influence of Isaac Newton’s Theology, by James E.Force and Richard H. Popkins, Kulwar Academic publishers, page 3
3. Newton, Maimonides, and Esoteric Knowledge
4. Essays on the Context, Nature, and Influence of Isaac Newton’s Theology, page 4
5. Newton, Maimonides, and Esoteric Knowledge
6. Isaac Newton’s Temple of Solomon and His Reconstruction of the Sacred Cubit, Tessa Morrison, Springer Science and Business Media, page 36
7. Judaism in the Theology of Sir Isaac Newton, Matt Goldish, Springer Netherlands, https://archive.org/details/springer_10.1007-978-94-017-2014-4
8. The Newton you Never Knew. See also footnote 6
9. The Essential Keynes, by John Maynard Keynes, Penguin Random House. Newton’s technical studies in alchemy, a mystical, archaic study about turning lead into gold, prompted further criticism.

 

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

ゼロ除算の発見と重要性を指摘した：日本、再生核研究所

 

 

ゼロ除算関係論文・本

 

ゼロ除算算法を使うとどうでしょうか？？？

有限の値が出るのですがいかがでしょうか・・

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\begin{document}

\title{\bf Announcement 448:\\  Division by Zero;\\

 Funny History and New World}

\author{再生核研究所}

\date{2018.08.20}

 

 

\maketitle

 

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\def\z{\zeta}

\def\rA{r_{\rm A}}

 

 

{\bf Abstract: }  Our division by zero research group wonder why our elementary results may still not be accepted by some wide world and very recently in our Announcements: 434 (2018.7.28),

437 (2018.7.30),

438(2018.8.6), \\

441(2018.8.9),

442(2018.8.10),

443(2018.8.11),

444(2018.8.14),

in Japanese, we stated their reasons and the importance of our elementary results. Here, we would like to state their essences. As some essential reasons, we found fundamental misunderstandings on the division by zero and so we would like to state the essences and the importance of our new results to human beings over mathematics.

 

We hope that:

 

close the mysterious and long history of division by zero that may be considered as a symbol of the stupidity of the human race and open the new world since Aristotle-Eulcid.

 

From the funny history of the division by zero, we will be able to realize that

 

 human beings are full of prejudice and prejudice, and are narrow-minded, essentially.

 

\medskip

 

 

\section{Division by zero}

 

The division by zero with mysterious and long history was indeed trivial and clear as in the followings:

\medskip

 

By the concept of the Moore-Penrose generalized solution of the fundamental equation $az=b$, the division by zero was trivial and clear  as $b/0=0$ in the {\bf generalized fraction} that is defined by the generalized solution of the equation $az=b$.

 

Note, in particular, that there exists a uniquely determined solution for any case of the equation $az=b$ containing the case $a=0$.

 

People, of course, consider as the division $b/a$ that it is the solution of the equation $ az =b$ and if $a=0$ then $0 \cdot z =0$ and so, for $b\ne0$ we can not consider the fraction $a/b$. We have been considered that the division by zero $b/0$ is impossible for mysteriously long years, since the document of zero in India in AD 628. In particular, note that Brahmagupta (598 -668 ?) established  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. However, he did not give its reason and did not consider  the importance case $1/0$ and the general fractions $b/0$. The division  by zero was a symbol for {\bf impossibility} or to consider the division by zero was {\bf not permitted}. For this simple and clear conclusion, we did not definitely consider more on the division by zero. However, we see many and many formulas appearing the zero in denominators, one simple and typical example is in the function $w=1/z$ for $z=0$.

We did not consider the function at the origin $z=0$.

 

In this case, however, the serious interest happens in many physical problems and also in computer sciences, as we know.

 

When we can not find the solution of the fundamental equation $az=b$, it is fairly clear to consider the Moore-Penrose generalized solution in mathematics. Its basic idea and beautiful mathematics will be definite.

Therefore, we should consider the generalized fractions following the Moore-Penrose generalized inverse. Therefore, with its meaning and definition we should consider that $b/0=0$.

 

It will be very  curious that we know very well the Moore-Penrose generalized inverse as a very fundamental and important concept, however, we did not consider the simplest case $ az =b$.

 

Its reason may be considered as follows: We will  consider or imagine that the fraction $1/0$ may be like infinity or ideal one.

 

For the fundamental function $W =1/ z $ we did not consider any value at the origin $z = 0$. 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 have to 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, Euclidian geometry,  analytic geometry, complex analysis and the theory of differential equations in an undergraduate level and furthermore to our basic ideas for the space and universe.

 

 For the extended complex plane, we consider its stereographic  projection mapping as the Riemann sphere and the point at infinity is realized as the north pole in the Alexsandroff’s one point compactification.

The Riemann sphere model gives  a beautiful and complete realization of the extended complex plane through the stereographic projection mapping and the mapping has beautiful properties like isogonal (equiangular) and
circle to circle correspondence (circle transformation). Therefore, the Riemann sphere is a very classical concept \cite{ahlfors}.

\medskip

 

Now, with the division by zero we have to admit the strong discontinuity at the point at infinity. To accept this strong discontinuity seems to be very difficult, and therefore we showed many and many examples for giving the evidences over $800$ items.

 

\medskip

 

We back to our general fractions $1/0=0/0=z/0=0$ for its importances.

 

\medskip

 

H. Michiwaki and his 6 years old daughter Eko Michiwaki stated that in about three weeks after the discovery of the division by zero that

division by zero is trivial and clear from the concept of repeated subtraction and they showed the detailed interpretation of the general fractions. Their method is a basic one and it will give a good introduction of division and their calculation method of divisions.

 

 We can say that division by zero, say $100/0$ means that we do not divide $100$ and so the number of the divided ones is zero.

 

\medskip

 

Furthermore,

recall the uniqueness theorem by S. Takahasi on the division by zero:

\medskip

 

 {\bf  Proposition 1.1 }{\it Let F be a function from  ${\bf C }\times {\bf C }$  to ${\bf C }$ satisfying

$$

F (b, a)F (c, d)= F (bc, ad)

$$

for all

$$

a, b, c, d  \in {\bf C }

$$

and

$$

F (b, a) = \frac {b}{a },  \quad   a, b  \in  {\bf C }, a \ne 0.

$$

Then, we obtain, for any $b \in {\bf C } $

$$

F (b, 0) = 0.

$$

}

 

 

 Note that the complete proof of this proposition is simply given by  2 or 3 lines. 

 In the long mysterious history of the division by zero, this proposition seems to be decisive.

Indeed,  Takahasi’s assumption for the product property should be accepted for any generalization of fraction (division). Without the product property, we will not be able to consider any reasonable fraction (division).

 

Following  Proposition 1.1, we  should {\bf define}

$$

F (b, 0) = \frac{b}{0} =0,

$$

and consider, for any complex number $b$, as $0$;

that is, for the mapping

\begin{equation}

W = f(z) = \frac{1}{z},

\end{equation}

the image of $z=0$ is $W=0$ ({\bf should be defined from the form}).

 

\medskip

 

Furthermore,

the simple field structure containing division by zero was established by M. Yamada.

\medskip

 

 

In addition, for the fundamental function  $f(z) = 1/z$, note that

the function is odd function

$$

f(z) = – f(-z)

$$

and if the function may be extended as an odd function at the origin $z=0$, then the identity $f(0) = 1/0 =0$ has to be satisfied. Further, if the equation

$$

\frac{1}{z} =0

$$

has a solution, then the solution has to be $z=0$.

\medskip

 

 

\section{Division by zero calculus}

 

As the number system containing the division by zero, the Yamada field structure is complete.

 

  However, for applications of the division by zero to {\bf functions}, we  need the concept of the division by zero calculus for the sake of uniquely determinations of the results and for other reasons.

 

For example,  for the typical linear mapping

\begin{equation}

W = \frac{z – i}{z + i},

\end{equation}

it gives a conformal mapping on $\{{\bf C} \setminus \{-i\}\}$ onto $\{{\bf C} \setminus \{1\}\}$ in one to one and from \begin{equation}

W = 1 + \frac{-2i}{ z – (-i)},

\end{equation}

we see that $-i$ corresponds to $1$ and so the function maps the whole $\{{\bf C} \}$ onto $\{{\bf C} \}$ in one to one.

 

Meanwhile, note that for

\begin{equation}

W = (z – i) \cdot \frac{1}{z + i},

\end{equation}

if we enter $z= -i$ in the way

\begin{equation}

[(z – i)]_{z =-i} \cdot  \left[ \frac{1}{z + i}\right]_{z =-i}  = (-2i)  \cdot 0=  0,

\end{equation}

we have another value.

\medskip

 

In many cases, the above two results will have practical meanings and so, we will need to consider many ways for the application of the division by zero and we will need to check the results obtained, in some practical viewpoints. We referred to this delicate problem with many examples.

 

 

Therefore, we will introduce the division by zero calculus that give important values for functions.  For any Laurent expansion around $z=a$,

\begin{equation}

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 obtain the identity, by the division by zero

\begin{equation}

f(a) =  C_0.

\end{equation}

Note that here, there is no problem on any convergence of the expansion (2.5) at the point $z = a$, because all the terms $(z – a)^n$ are zero at $z=a$ for $n \ne 0$.

\medskip

 

For the correspondence (2.6) for the function $f(z)$, we will call it {\bf the division by zero calculus}. By considering the formal derivatives in (2.5), we {\bf can define any order derivatives of the function} $f$ at the singular point $a$; that is,

$$

f^{(n)}(a) = n! C_n.

$$

 

\medskip

 

 

 

{\bf Apart from the motivation, we  define the division by zero calculus by (2.6).}

 With this assumption, we can obtain many new results and new ideas. However, for this assumption we have to check the results obtained  whether they are reasonable or not. By this idea, we can avoid any logical problems.  —  In this point, the division by zero calculus may be considered as an axiom.

\medskip

This paragraph is very important. Our division by zero is just definition and the division by zero is an assumption. Only with the assumption and definition of the division by zero calculus, we can create and enjoy our new mathematics. Therefore, the division by zero calculus may be considered as a new axiom.

 

 Of course, its strong motivations were given. We did not consider any value  {\bf at  the singular point} $a$ for the Laurent expansion (2.5). Therefore, our division by zero is a new mathematics entirely and isolated singular points are a new world for our mathematics.

We had been considered properties of analytic functions {\bf  around their isolated singular points.}

 

The typical example of the division zero calculus is $\tan (\pi/2) = 0$ and the result gives great impacts to analysis and geometry.

See the references for the materials.

\medskip

 

For an identity, when we multiply zero, we obtain  the zero identity that is a trivial.

We will consider the division by zero to an equation.

 

For example, for the simple example for the line equation on the $x, y$ plane

$$

 ax + by + c=0

$$

we have, formally

$$

x + \frac{by + c}{a} =0,

$$

and so, by the division by zero, we have, for $a=0$, the reasonable result

$$

x = 0.

$$

 

However, from

$$

\frac{ax + by}{c} + 1 =0,

$$

for $c=0$, we have the contradiction, by the division by zero

$$

1 =0.

$$

 For this case, we can consider that

$$

\frac{ax + by}{c} + \frac{c}{c} =0,

$$

that is always valid. {\bf In this sense, we can divide an equation by zero.}

 

\section{Conclusion}

 

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.

 

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.

 

From the mysterious history of the division by zero, we will be able to study what are human beings and about our narrow-minded.

 

\bibliographystyle{plain}

\begin{thebibliography}{10}

 

\bibitem{ahlfors}

L. V. Ahlfors, Complex Analysis, McGraw-Hill Book Company, 1966.

 

\bibitem{ass}

H. Akca, S. Pinelas and S. Saitoh, The Division by Zero z/0=0 and Differential Equations (materials).

International Journal of Applied Mathematics and Statistics, Int. J. Appl. Math. Stat. Vol. 57; Issue No. 4; Year 2018, ISSN 0973-1377 (Print), ISSN 0973-7545 (Online).

 

\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{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{os18april}

H.  Okumura and S. Saitoh,

Harmonic Mean and Division by Zero,

Dedicated to Professor Josip Pe$\check{c}$ari$\acute{c}$ 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)(in press).

 

 

 

 

 

\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{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 (Draft) (210 pages): 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

 

 

\end{thebibliography}

 

\end{document}

再生核研究所声明 427(2018.5.8): 神の数式、神の意志　そしてゼロ除算

 

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 
&t=3318s 
〔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 
 

NHKスペシャル　神の数式番組を繰り返し拝見して感銘を受けている。素晴らしい映像ばかりではなく、内容の的確さ、正確さに、ただただ驚嘆している。素晴らしい。

ある物理学の本質的な流れを理解し易く表現していて、物理学の着実な発展が良く分かる。

原爆を作ったり、素粒子を追求していたり、宇宙の生成を研究したり、物理学者はまるで、現代の神官のように感じられる。素粒子の世界と宇宙を記述するアインシュタインの方程式を融合させるなど、正に神の数式と呼ぶにふさわしいものと考えられる。流れを拝見すると物理学は適切な方向で着実に進化していると感じられる。神の数式に近づいているのに　野蛮なことを繰り返している国際政治社会には残念な気持ちが湧いて来る。ロシアの天才物理学者の終末などあまりにも酷いのではないだろうか。世界史の進化を願わざるを得ない。

アインシュタインの相対性理論は世界観の変更をもたらしたが、それに比べられるオイラーの公式は数学全般に大きな変革をもたらした：　

 

With this estimation, we stated that the Euler formula

$$

e^{\pi i} = -1

$$

is the best result in mathematics in details in：　No.81, May 2012 (pdf 432kb)

余りにも神秘的な数式のために、アインシュタインの公式 E= mc^2　と並べて考えられる　神の意志　が感じられるだろう。　ところで、素粒子を記述する方程式とアインシュタインの方程式を融合したら、　至る所に1/0 が
現れて　至る所無限大が現れて計算できないと繰り返して述べられている。しかしながら、数学は既に進化して、1/0=0　で無限大は　実はゼロだった。　驚嘆すべき世界が現れた。しかしながら、数学でも依然として、rがゼロに近づくと　無限大に発散する事実が有るので、弦の理論は否定できず、問題が存在する。さらに、形式的に発散している場合でも、ゼロ除算算法で、有限値を与え、特異点でも微分方程式を満たすという新しい概念が現れ、局面が拓かれたので、数学者ばかりではなく、物理学者の注意を喚起して置きたい。

物理学者は、素粒子の世界と巨大宇宙空間の方程式を融合させて神の方程式を目指して研究を進めている。数学者はユークリッド以来現れたゼロ除算1/0と空間の新しい構造の中から、神の意志を追求して　新しい世界の究明に乗り出して欲しいと願っている。いみじくもゼロ除算は、ゼロと無限大の関係を述べていて、素粒子と宇宙論の類似を思わせる。

人の生きるは、真智への愛にある、すなわち、事実を知りたい、本当のことを知りたい、高級に言えば　神の意志　を知りたいということである。　そこで、我々のゼロ除算についての考えは真実か否か、広く内外の関係者に意見を求めている。関係情報はどんどん公開している。　ゼロ除算の研究状況は、

数学基礎学力研究会　サイトで解説が続けられている：

また、o　に　関連情報がある。

以　上

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

とても興味深くみました： 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 ↓↓↓ ゼロ除算の発見と重要性を指摘した：日本、再生核研究所 　　2014年2月2日

 

Can You See The Light? Researchers Reveal Quantum Magnets That Mimic Light

What is light? It seems like a simple question at first sight, but it has kept on captivating the hearts of great scientists for centuries.

With collaborative research by scientists of Okinawa Institute of Science and Technology (OIST), we have made an abstract theory on the quantum properties of magnets a verifiable hypothesis about a new kind of light, A twist was added.

Ever since Isaac Newton refracted light through the prism in 1672, scientists have been divided into particle theories of light as particles and wave theory as waves. Although light travels linearly like particles, Newton’s experiment also showed that light has frequency and wavelength as well as acoustic waves as well.

  About two hundred years later, Scottish physicist James Clark Maxwell noticed that light is composed of varying electric and magnetic fields, presenting a new view to elucidate the mystery of light did. Eventually in the 20th century, for the first time by Einstein’s research, light is understood to be composed of basic particles called photons that behave like both particles and waves.

Furthermore, this discovery also encouraged new developments in quantum mechanics to explain the behavior of particles and energy at atomic or atomic levels

Furthermore, in recent years in the second half of the 20th century, physicists began exploring the phenomenon “emergence.” Emergence means, for example, that there is a large crowd of many people. It is also possible for unpredictable composition to appear due to the behavior of the crowd and the behavior of one of them being different. In this way, emergent research shows the possibility of unpredictable movement by each particle in a large particle group, raising a new perspective on the new physical law and the conventional law constructed by it . And one of the questions asked was “Does emergent light exist?”

Here is Professor Nick Shannon of OIST, Doctoral Student Yang Han belonging to the quantum theory unit led by Professor, and their collaborators in Switzerland and the United States will be on their way. Because their recent research results focus on strange magnetic bodies known as spin ice. This spin ice was completely removed from the conventional magnetic order and opened a new door to the world of quantum physics.

For example, there are general magnets to attach to a refrigerator at home. In order for such magnets to “stick” to metal objects or the like, magnetic atoms in the magnet form a small magnetic field, which cooperate to create a larger magnetic field. In addition, the magnetic force is established by arranging the small magnetic fields due to magnetic atoms to face the same direction.

 On the other hand, in the case of spin ice, a magnetic field that varies at the atomic level is formed by cooperative action, even though the magnetic atoms are not aligned.

 Recently researchers realized that it was possible to introduce an emergent electric field into spin ice by the quantum effect at low temperature, which led to surprising results. The emergent electric field and the magnetic field combine to cause magnetic excitation and they act exactly like photons of light.

“It behaves like light, but you can not see with the naked eye,” Professor Shannon says. “Imagine the situation where spin ice crystal is a small universe with its own natural law and you are looking at it from the outside, how can you figure out what is going on inside?” I will.

2012, Owen Benton Dr. was a student of Shannon professor and then PhD, by bouncing neutrons from magnetic atoms in the crystal, a method of detecting the light in the quantum spin ice raised was. Researchers predicted the characteristic traces of how crystals absorb neutron energy and show the existence of emergent electrodynamics in quantum spin ice.

In the paper published in Nature Physics magazine , the authors report that this trace was successfully observed with a substance called praseodymium · hafnate (Pr 2 Hf 2 O 7 ).

To find traces of emergent light with actual materials, it was very difficult to work with cold with impurities or defects and at a low temperature of 50 milli Kelvin (absolute zero to less than 0.1 degrees)

The research team of Dr. Romaine Sybil of Switzerland’s Paul Scherrer Institute (PSI) worked with researchers at Warwick University in the UK to finally complete the quantum spin ice material that can verify this hypothesis We succeeded in making crystals.

Professor Shannon said, “It is a very beautiful material like a precious stone,” he said, “It is also amazing to be one big perfect crystal.”

Dr. Sybil brought this crystal to Laue-Langevin Institute (ILL) in Grenoble city, France and Oak Ridge National Laboratory (ORNL) in Tennessee, USA, and the specially developed neutron spectrometer We used

In an experiment with great difficulty, Dr. Sybil ‘s team succeeded in selectively reflecting different types of neutrons by using a row of 960 super mirrors coated with iron, cobalt, or vanadium did. Several of the supermirrors were developed by PSI belonging to Dr. Civil and HYSPEC instrument (ORNL) was used to perform 3D analysis of the reflection pattern

We were able to measure the polarization of the scattered particles through the mapping of the scattered neutrons obtained from IN5 and succeeded in mapping the traces of energy generated from those particles

As a result, the theory of Dr. Benton and Professor Shannon was surprisingly similar to the energy diagram obtained in the experiment (see above figure). In the energy diagram imaging this neutron reflex, we saw the so-called “pinch point” (a structure whose center is constricted like a bow tie), which is a feature of quantum spin ice. And as spin ice was scanned at low temperature, these pinch points disappeared as strongly suggesting the emergence of emergent light.

Mr. Yang Han of the same research team measured the speed of emergent light by analyzing experimental data while working on the theory of this phenomenon. The speed is modest at 3.6 meters per second, which is about as fast as finishing a marathon in four hours. By the way, photons of light that we take sunbathing etc. run the same distance less than 0.001 seconds.

“This substance acts like a microcosm with unique light and charged particles, but I think it is wonderful,” Han said.

“At this time, there is no known way to explain these results without using quantum mechanics, so we can say that we actually showed the existence of emergent light. “Professor Shannon said.

SOURCE: Okinawa Institute of Science and Technology (OIST)

 

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：

ゼロ除算の発見と重要性を指摘した：日本、再生核研究所

 

ゼロ除算関係論文・本

 

\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、
 [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

 

&nbs
p;

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

 

 

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

                                                                                                                                             

 

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. 
 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

 

2018年05月28日(月)
テーマ：

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

 

 

On top of all that, electric skateboards require a lot less physical effort because they obviously move without the help of your feet, but thanks to a wireless remote controller that sends signals to the attached battery on the board’s back, according to the buttons you push. Hence the constant craving for excitement and rush. The consequence of such an attitude forms the second reason for creating the electric skateboards: because everything is so simple we now get too easily bored and ultimately turn into adrenaline junkies.What is a rush if not an electric feeling? It is a sudden movement, a surging emotion, a sudden, brief exhilaration and it can all have one cause: the use of electric skateboards. First and foremost the fact that everything these days is becoming electronic, digital, virtual or mechanical. Electric skateboards are the perfectly balanced combination of the two previously mentioned human conditions: the need for simplicity and the one for speed. Nothing less of transportation devices, electric skateboards allow you to cruise the city all the while being capable of inducing stronger sensations if used properly. . Thrill seekers have a pretty wide range of products they can choose from, not to mention the possibility of customizing their machines. The considerably bigger wheels electric skateboards use also add a notable number of surfaces somebody can explore with them. Although electric skateboards can reach higher speeds ‘ up to 20 miles per hour when compared to regular skates, the smaller probability for injury is due to the fact that electric skateboards unable one to perform the tricks and schemes the others could, being often enough compared to Segways. It is the natural way of things, to evolve, to transform into better, bigger, more complex designs. They might not represent the biggest rush one can get on dry land but are definitely worth the ride especially if you get a bunch of friends to join the fun. For the unlikely few who fail to figure out what that might be, wakeskating is a water sport and an adaptation of wakeboarding but unlike in it, the rider is not bound to the board in any way. The extent of the risks involved is really a notch lower than the one a person using a normal skateboard faces. The invention of electric skateboards must have had two logical reasons. As compensation for not having all the properties as old school type skateboards, electric skateboards offer the long searched for sensation of speed all the while offering much more stability. It is also human nature to want to transform all that we can in practical, simpler things in order to make life easier. Nevertheless, no matter what you compare them to, electric skateboards are in. They might not last as long as the bicycle but they are undoubtedly an extremely fun way to pass the time and wonder the streets without getting bored. Actually, electric skateboards have not only been compared to normal non mechanical skateboards but also to the sport we call wakeskating.