Crimes committed in the name of religion – the Inquisition
August 28, 2018, 9:28 pm
Dr. V.J.M. de Silva
"I believe the idea that Galileo’s trial was a kind of Greek tragedy, a showdown between blind faith and enlightened reason, to be naively erroneous." Arthur Koestler, The Sleepwalkers
On 6th June 2018, I wrote an article in the Island Midweek Review titled ‘Crimes committed in the name of Religion – some rethinking’. In it I wrote about the Crusades and its background. I also mentioned the other "blots on Christianity" viz. the Inquisition, colonial exploitation and anti-Semitism. In this article I deal with the Inquisition.
Reopening the Galileo case – The "Galileo affair" is perhaps the most commonly discussed case of conflict between science and religion. According to widespread popular belief, Galileo was a martyr of science who was tortured and imprisoned by the Roman Catholic Church. This of course is not factual. . For nearly 2000 years before Galileo, the accepted theory was the one propounded by Aristotle (384- 322 BC) – the geocentric (earth as the centre of the universe). This was later refined mathematically by Claudius Ptolemy (c AD 100-170) a Greco-Roman mathematician, astronomer, geographer.
However, in 1543 Nicolaus Copernicus (1473 -1543), a Polish church official and accomplished astronomer, published a book, On the Revolutions of the Celestial Orbs – which he dedicated to Pope Paul III, (Pope:1534-49), in which he took the heliocentric system and defended it as a true description of the universe. He located the sun at the center of the universe, and the earth and its moon in motion around the sun. Because his book was highly technical, written for a small audience of mathematically proficient astronomers, it was little known and less read. Copernicus had no new evidence to justify his theory. He adopted it because it had greater explanatory power than Ptolemy’s. True heliocentrism wasn’t conclusively proved until some 200 years later – (James C. Ungureanu, Exploring the Relations between Science, Religion, and Culture, 1913).
URL https://jamescungureanu.wordpress.com/2013/04/30/myths-about-science-and-religion-that-galileo-was-tortured-and-impris..
Galileo Galilei (1564-1642) was a firm believer in God and the Bible, and remained so all of his life. Once, a supporter of Ptolemy’s geocentric theory, he became convinced that Copernicus was right. At that time the prevailing view was that the Copernican theory, though useful for calculating the motions of heavenly bodies, was not persuasive enough to discard the geocentric theory altogether. Having developed a more powerful telescope than others of his day, he was able make observations which were consistent with the Copernican theory.
He took these observations to the Jesuit priests (Collegio Romano), who were among the leading astronomers of the day, and they agreed that the case for the heliocentric theory was strengthened. The Jesuits told Galileo that the Church was divided on this issue. They did not think that Galileo had clinched the case. Tycho Brahe (1546- 1601), Danish nobleman and leading astronomer of the day, also agreed and continued to support the geocentric theory.
When Galileo’s lectures on the heliocentric theory were reported to head of the Inquisition, the learned theologian Cardinal Robert Bellarmine, met Galileo – (not normal procedure, but Galileo was a celebrity). It was Galileo who said, "The Bible tells you how to go to heaven, not how the heavens go." Indeed, Biblical language which in some places is equivocal, should not be mistaken for statements on cosmology. Regarding the cosmos, it is a myth that Christians at one time believed in a ‘flat earth’. The Bible says no such thing. When in Psalm 19:6, the Bible talks of the sun ‘rising’, it is only giving a description as it appears to the observer, rather than implying commitment to a particular solar and planetary theory. Even today, we speak of "sunrise" and "sunset" - (Jeffrey Burton Russell, "The myth of the Flat Earth") –
URL http://www.veritas-ucsb.org/library/russell/FlatEarth.html
In the beginning Galileo had the support of religious intellectuals, the astronomers of the Jesuit institution, the Collegio Romano. He was opposed mainly by secular philosophers, who were very angry at his criticism of Aristotle. In his famous Letter to the Grand Duchess Christina (1615), he says the academic professors were opposed to him and they were trying to influence the church authorities to speak against him. Aristotelian philosophy, with its acceptance of the geocentric theory, was the then reigning paradigm (worldview). The general trend among scientists is to oppose anything against the reigning paradigm; criticizing it is indeed risky - (just as today Darwin’s Theory is defended against the more recent Intelligent Design concept).
Cardinal Bellarmine’s Directive - What Bellarmine observed was that there could be no real conflict between nature and scripture. If natural evidence shows that we were wrong, then we need to revise our interpretation of scripture and acknowledge our mistake. As he said, "But this is not a thing to be done in haste, and as for myself, I shall not believe that there are such proofs until they are shown to me . . . . . But first let us make sure that there is in fact conclusive proof before we start changing scriptural interpretation."– (James Broderick, Robert Bellarmine: Saint and Scholar, 1961).
At this stage some reflection on Cardinal Bellarmine’s directive is pertinent. He says if the heliocentric theory could be truly demonstrated, it would be better to say that we do not understand scripture than to say that what has been demonstrated is false. So, the Cardinal was willing to say that we might have misinterpreted scripture and acknowledge our mistake, in order to uphold science. Some of Galileo’s beliefs were of course wrong. He held that the entire universe revolved around the sun in circular (not elliptical) orbits, and that tides were caused by the rotation of the earth.
In 1616, Cardinal Bellarmine, on directives from the Inquisition, proposed a solution. Given the inconclusive evidence, and the sensitivity of the religious issues involved, Galileo should not teach or promote heliocentrism. The decree did not prevent Galileo from discussing heliocentrism hypothetically. Galileo, a practicing Catholic, agreed.
Galileo’s mistakes – For several years Galileo kept his word and did not advocate the heliocentric theory in public. In 1623 Cardinal Maffeo Barberini became Pope Urban VIII. He was a scientific "progressive", and a fan of Galileo, who now thought he could openly advocate heliocentrism. In 1632 Galileo published his book Dialogue Concerning the Two Chief World Systems, which caricatured two figures, himself and a representative of the pope. To dramatize the contrast, Galileo gave the pope character the name Simplicio, which in Italian means "simpleton". The dialogue consists of foolish claims by Simplicio, elegantly refuted by the character speaking for Galileo. The pope of course was not amused! In addition he advanced his own theories on theological matters. This displeased the Church. Further, in a debate on the topic of comets with a Jesuit mathematics professor, Orazio Grassi, who had written on the subject, Galileo attacked his opponent on a personal level, loosing even friends in the Collagio Romano. Galileo was arrogant and impetuous by nature and made enemies easily.
This was also the age of the Reformation, and the Thirty Year War (1618 -1648), when Catholics were fighting against Protestants in Germany. However, as the Thirty Years’ War evolved, it became less about religion and more about which group would ultimately govern Europe. Millions died in this war. Pope Urban was eager to show the Vatican’s fidelity to scripture, which was under attack for not taking the Bible seriously. The geocentric theory appeared to be in harmony with scripture. The Inquisition summoned Galileo again, and being found guilty of supporting the heliocentric theory, was asked to recant, which he did. He was not charged with heresy, never placed in a dungeon or tortured. He was under "house arrest" and lived in the villas of friends and died peacefully in his bed. He was at liberty to continue with other researches, which he did.
The Inquisition – This began in 1163, when Pope Alexander instructed the bishops to discover evidence of heresy and take action. Heresies started creeping into the Church from the time of the Church Fathers. Those like Justin Martyr - (AD 100-165) and Tertullian (ca. AD 150-225) have mentioned these in their writings. In the 12th century, the papacy was concerned about the heresy in southern France among the Albigenses. Traditional means of persuasion like sending missionaries did not work. The second wave of the inquisition was in 1472 when Ferdinand and Isabella started the Spanish Inquisition, and the third and final in 1542 when Pope Paul III wanted to hunt down Calvinists. So, in the past we have the sad spectacle of Catholics who call themselves Christians, having persecuted Protestants who call themselves Christians. It is indeed laudable that Pope John Paul II apologized on behalf of the church for the wrongs done to Galileo and other crimes committed by the church in the past. He said in his statement "that the church is holy, but is stained by the sins of its children".
Conclusion – The Inquisition is a tragedy that Christians cannot run away from. In those times, religion and politics were bound up together. However, every one of the combatants, whether church official or disciple of Galileo, called himself a Christian; and all, without exception, acknowledged the authority of Scripture. Although the topic I have dealt with is one concerning Catholics, I must say I am not a Catholic (being an Anglican). My purpose in writing this article is to correct some misinformation regarding the "Galileo affair" repeatedly mentioned by some writers.
These events took place in Europe. Today, the typical Christian is no longer European. He lives in a developing country, speaks a non-European language and is often under threat of persecution. Talking of persecution, millions of Christians themselves have been victims of brutal persecution through the ages, continuing to the present day in some places. There have been more Christian martyrs in the 20th century than in any other time. To this very day Christians are being killed for their faith around the world. So, the Inquisition is by far an exception in church history, not the norm.
(Most of the facts in this article have been taken from Dinesh D’Souza, What’s so great about Christianity, 2008)http://island.lk/index.php?page_cat=article-details&page=article-details&code_title=190337
ゼロ除算の発見は日本です：
∞？？？
∞は定まった数ではない・
人工知能はゼロ除算ができるでしょうか：
とても興味深く読みました：2014年2月2日 4周年を超えました：
ゼロ除算の発見と重要性を指摘した：日本、再生核研究所
ゼロ除算関係論文・本
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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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{\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.
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\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
https://www.youtube.com/watch?v=iQld9cnDli4
〔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
https://www.youtube.com/watch?v=DvyAB8yTSjs&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
https://www.youtube.com/watch?v=KjvFdzhn7Dc
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
https://www.youtube.com/watch?v=fWVv9puoTSs
https://www.youtube.com/watch?v=iQld9cnDli4
〔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
https://www.youtube.com/watch?v=DvyAB8yTSjs&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
https://www.youtube.com/watch?v=KjvFdzhn7Dc
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
https://www.youtube.com/watch?v=fWVv9puoTSs
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：http://www.mirun.sctv.jp/~suugaku/
また、ohttp://okmr.yamatoblog.net/ 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∞=0log0=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
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∞=0log0=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 ↓↓↓ https://juniperpublishers.com/bboaj/pdf/BBOAJ.MS.ID.555703.pdf 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
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