Show that for unsigned division by an even number, the shrxi instruction … Good code to divide takes a Knuthian hero, But even God can’t divide by zero!
Announcement 478: Who did derive first the division by zero 1/0 and the division by zero calculus $\tan(\pi/2)=0, \log 0=0$ as the outputs of a computer?
それゆえに ゼロ除算算法の概念による ゼロ除算の解明によって 初等数学は 広範な影響を受けることになったが、不変な筈のユークリット幾何学でさえ、面目を一新するような革命が起きている： viXra:2106.0108 submitted on 2021-06-19 20:06:05, Division by Zero Calculus in Figures – Our New Space Since Euclid –
Geometry and division by zero calculus. International Journal of Division by Zero Calculus, 1(1), pp.1-36. （https://romanpub.com/dbzc.php）
簡単な図版の例が 奥村 博氏の論文の中に見られる： iXra:2106.0108 submitted on 2021-06-19 20:06:05, Division by Zero Calculus in Figures – Our New Space Since Euclid Geometry and division by zero calculus. International Journal of Division by Zero Calculus, 1(1), pp.1-36. （https://romanpub.com/dbzc.php）
Please look 1/0=0: As Fundamental of Mathematics, the division by zero was known as the generalized Moore-Penrose solution of the fundamental equation: ax=b.
Look the simple evidence of its importance: viXra:2010.0228 submitted on 2020-10-28 21:39:06, Division by Zero Calculus and Euclidean Geometry – Revolution in Euclidean Geometry
Show that for unsigned division by an even number, the shrxi instruction … Good code to divide takes a Knuthian hero, But even God can’t divide by zero!
Announcement 478: Who did derive first the division by zero 1/0 and the division by zero calculus $\tan(\pi/2)=0, \log 0=0$ as the outputs of a computer?
それゆえに ゼロ除算算法の概念による ゼロ除算の解明によって 初等数学は 広範な影響を受けることになったが、不変な筈のユークリット幾何学でさえ、面目を一新するような革命が起きている： viXra:2106.0108 submitted on 2021-06-19 20:06:05, Division by Zero Calculus in Figures – Our New Space Since Euclid –
Geometry and division by zero calculus. International Journal of Division by Zero Calculus, 1(1), pp.1-36. （https://romanpub.com/dbzc.php）
簡単な図版の例が 奥村 博氏の論文の中に見られる： iXra:2106.0108 submitted on 2021-06-19 20:06:05, Division by Zero Calculus in Figures – Our New Space Since Euclid Geometry and division by zero calculus. International Journal of Division by Zero Calculus, 1(1), pp.1-36. （https://romanpub.com/dbzc.php）
Please look 1/0=0: As Fundamental of Mathematics, the division by zero was known as the generalized Moore-Penrose solution of the fundamental equation: ax=b.
Look the simple evidence of its importance: viXra:2010.0228 submitted on 2020-10-28 21:39:06, Division by Zero Calculus and Euclidean Geometry – Revolution in Euclidean Geometry
Show that for unsigned division by an even number, the shrxi instruction … Good code to divide takes a Knuthian hero, But even God can’t divide by zero!
Announcement 478: Who did derive first the division by zero 1/0 and the division by zero calculus $\tan(\pi/2)=0, \log 0=0$ as the outputs of a computer?
それゆえに ゼロ除算算法の概念による ゼロ除算の解明によって 初等数学は 広範な影響を受けることになったが、不変な筈のユークリット幾何学でさえ、面目を一新するような革命が起きている： viXra:2106.0108 submitted on 2021-06-19 20:06:05, Division by Zero Calculus in Figures – Our New Space Since Euclid –
Geometry and division by zero calculus. International Journal of Division by Zero Calculus, 1(1), pp.1-36. （https://romanpub.com/dbzc.php）
簡単な図版の例が 奥村 博氏の論文の中に見られる： iXra:2106.0108 submitted on 2021-06-19 20:06:05, Division by Zero Calculus in Figures – Our New Space Since Euclid Geometry and division by zero calculus. International Journal of Division by Zero Calculus, 1(1), pp.1-36. （https://romanpub.com/dbzc.php）
Please look 1/0=0: As Fundamental of Mathematics, the division by zero was known as the generalized Moore-Penrose solution of the fundamental equation: ax=b.
Look the simple evidence of its importance: viXra:2010.0228 submitted on 2020-10-28 21:39:06, Division by Zero Calculus and Euclidean Geometry – Revolution in Euclidean Geometry
Show that for unsigned division by an even number, the shrxi instruction … Good code to divide takes a Knuthian hero, But even God can’t divide by zero!
Show that for unsigned division by an even number, the shrxi instruction … Good code to divide takes a Knuthian hero, But even God can’t divide by zero!
Now that we’ve reached the point where people who have been calling the rest of us “sheep” for the last year are now taking medicine designed for (wait for it)–sheep–I’m reasonably sure that division by zero is now possible.
Now that we've reached the point where people who have been calling the rest of us "sheep" for the last year are now taking medicine designed for (wait for it)–sheep–I'm reasonably sure that division by zero is now possible.
— Dteve 🇺🇦🏳️🌈🇺🇦🏳️🌈🇺🇦 🏳️🌈🇺🇦 🏳️🌈 (@steveturner2112) September 4, 2021
Hell is the Absence of God (if that’s the one on angels you are talking about) is super good! I also really like Division by Zero (cw: discussion of suicide) and the most of the ones in “stories of your life and others”
Hell is the Absence of God (if that’s the one on angels you are talking about) is super good! I also really like Division by Zero (cw: discussion of suicide) and the most of the ones in “stories of your life and others”
Some examples of solving non-linear inequalities (full class, no edits)
The page “ゼロ除算” does not exist. You can ask for it to be created, but consider checking the search results below to see whether the topic is already covered.List of Steins;Gate episodesonce again. 23β “Divide by Zero” Transcription: “Zero josan” (Japanese: ゼロ除算) December 2, 2015 (2015-12-02) An alternate version of episode 23 aired as40 KB (521 words) – 14:14, 12 July 2021
Ancient Olympic Gamesオリュンピアにはエーリスの祭神・ゼウスの神殿があった。古代オリンピックは紀元前776年に古代ギリシアのエリス地方にあるオリンピアで始まったとされている。本競技会・祭典は紀元前8世紀から紀元後4世紀にかけて行われたもので、ギリシア四大大会（後述）のひとつである。https://ja.wikipedia.org/wiki/%E5%8F%A4%E4%BB%A3%E3%82%AA%E3%83%AA%E3%83%B3%E3%83%94%E3%83%83%E3%82%AF
In the philosophy of the ancient Greek Anaxagoras, as claimed by the Roman atomist Lucretius,[1] it was assumed that the atoms …. For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a …
The null set is conceptually similar to the role of the number “zero” as it is used in quantum field theory. In quantum field theory, one can take the empty set, the vacuum, and generate all possible physical configurations of the Universe being modelled by acting on it with creation operators, and one can similarly change from one thing to another by applying mixtures of creation and anihillation operators to suitably filled or empty states. The anihillation operator applied to the vacuum, however, yields zero.
Zero in this case is the null set – it stands, quite literally, for no physical state in the Universe. The important point is that it is not possible to act on zero with a creation operator to create something; creation operators only act on the vacuum which is empty but not zero. Physicists are consequently fairly comfortable with the existence of operations that result in “nothing” and don’t even require that those operations be contradictions, only operationally non-invertible.
It is also far from unknown in mathematics. When considering the set of all real numbers as quantities and the operations of ordinary arithmetic, the “empty set” is algebraically the number zero (absence of any quantity, positive or negative). However, when one performs a division operation algebraically, one has to be careful to exclude division by zero from the set of permitted operations! The result of division by zero isn’t zero, it is “not a number” or “undefined” and is not in the Universe of real numbers.
Just as one can easily “prove” that 1 = 2 if one does algebra on this set of numbers as if one can divide by zero legitimately3.34, so in logic one gets into trouble if one assumes that the set of all things that are in no set including the empty set is a set within the algebra, if one tries to form the set of all sets that do not include themselves, if one asserts a Universal Set of Men exists containing a set of men wherein a male barber shaves all men that do not shave themselves3.35.
It is not – it is the null set, not the empty set, as there can be no male barbers in a non-empty set of men (containing at least one barber) that shave all men in that set that do not shave themselves at a deeper level than a mere empty list. It is not an empty set that could be filled by some algebraic operation performed on Real Male Barbers Presumed to Need Shaving in trial Universes of Unshaven Males as you can very easily see by considering any particular barber, perhaps one named “Socrates”, in any particular Universe of Men to see if any of the sets of that Universe fit this predicate criterion with Socrates as the barber. Take the empty set (no men at all). Well then there are no barbers, including Socrates, so this cannot be the set we are trying to specify as it clearly must contain at least one barber and we’ve agreed to call its relevant barber Socrates. (and if it contains more than one, the rest of them are out of work at the moment).
Suppose a trial set contains Socrates alone. In the classical rendition we ask, does he shave himself? If we answer “no”, then he is a member of this class of men who do not shave themselves and therefore must shave himself. Oops. Well, fine, he must shave himself. However, if he does shave himself, according to the rules he can only shave men who don’t shave themselves and so he doesn’t shave himself. Oops again. Paradox. When we try to apply the rule to a potential Socrates to generate the set, we get into trouble, as we cannot decide whether or not Socrates should shave himself.
Note that there is no problem at all in the existential set theory being proposed. In that set theory either Socrates must shave himself as All Men Must Be Shaven and he’s the only man around. Or perhaps he has a beard, and all men do not in fact need shaving. Either way the set with just Socrates does not contain a barber that shaves all men because Socrates either shaves himself or he doesn’t, so we shrug and continue searching for a set that satisfies our description pulled from an actual Universe of males including barbers. We immediately discover that adding more men doesn’t matter. As long as those men, barbers or not, either shave themselves or Socrates shaves them they are consistent with our set description (although in many possible sets we find that hey, other barbers exist and shave other men who do not shave themselves), but in no case can Socrates (as our proposed single barber that shaves all men that do not shave themselves) be such a barber because he either shaves himself (violating the rule) or he doesn’t (violating the rule). Instead of concluding that there is a paradox, we observe that the criterion simply doesn’t describe any subset of any possible Universal Set of Men with no barbers, including the empty set with no men at all, or any subset that contains at least Socrates for any possible permutation of shaving patterns including ones that leave at least some men unshaven altogether.
I understand your note as if you are saying the limit is infinity but nothing is equal to infinity, but you concluded corretly infinity is undefined. Your example of getting the denominator smaller and smalser the result of the division is a very large number that approches infinity. This is the intuitive mathematical argument that plunged philosophy into mathematics. at that level abstraction mathematics, as well as phyisics become the realm of philosophi. The notion of infinity is more a philosopy question than it is mathamatical. The reason we cannot devide by zero is simply axiomatic as Plato pointed out. The underlying reason for the axiom is because sero is nothing and deviding something by nothing is undefined. That axiom agrees with the notion of limit infinity, i.e. undefined. There are more phiplosphy books and thoughts about infinity in philosophy books than than there are discussions on infinity in math books.
Lea esta bitácora en español There is a mathematical concept that says that division by zero has no meaning, or is an undefined expression, because it is impossible to have a real number that could be multiplied by zero in order to obtain another number different from zero. While this mathematical concept has been held as true for centuries, when it comes to the human level the present situation in global societies has, for a very long time, been contradicting it. It is true that we don’t all live in a mathematical world or with mathematical concepts in our heads all the time. However, we cannot deny that societies around the globe are trying to disprove this simple mathematical concept: that division by zero is an impossible equation to solve. Yes! We are all being divided by zero tolerance, zero acceptance, zero love, zero compassion, zero willingness to learn more about the other and to find intelligent and fulfilling ways to adapt to new ideas, concepts, ways of doing things, people and cultures. We are allowing these ‘zero denominators’ to run our equations, our lives, our souls. Each and every single day we get more divided and distanced from other people who are different from us. We let misinformation and biased concepts divide us, and we buy into these aberrant concepts in such a way, that we get swept into this division by zero without checking our consciences first. I believe, however, that if we change the zeros in any of the “divisions by zero” that are running our lives, we will actually be able to solve the non-mathematical concept of this equation: the human concept. >I believe deep down that we all have a heart, a conscience, a brain to think with, and, above all, an immense desire to learn and evolve. And thanks to all these positive things that we do have within, I also believe that we can use them to learn how to solve our “division by zero” mathematical impossibility at the human level. I am convinced that the key is open communication and an open heart. Nothing more, nothing less. Are we scared of, or do we feel baffled by the way another person from another culture or country looks in comparison to us? Are we bothered by how people from other cultures dress, eat, talk, walk, worship, think, etc.? Is this fear or bafflement so big that we much rather reject people and all the richness they bring within? How about if instead of rejecting or retreating from that person—division of our humanity by zero tolerance or zero acceptance—we decided to give them and us a chance? How about changing that zero tolerance into zero intolerance? Why not dare ask questions about the other person’s culture and way of life? Let us have the courage to let our guard down for a moment and open up enough for this person to ask us questions about our culture and way of life. How about if we learned to accept that while a person from another culture is living and breathing in our own culture, it is totally impossible for him/her to completely abandon his/her cultural values in order to become what we want her to become? Let’s be totally honest with ourselves at least: Would any of us really renounce who we are and where we come from just to become what somebody else asks us to become? If we are not willing to lose our identity, why should we ask somebody else to lose theirs? I believe with all my heart that if we practiced positive feelings—zero intolerance, zero non-acceptance, zero indifference, zero cruelty—every day, the premise that states that division by zero is impossible would continue being true, not only in mathematics, but also at the human level. We would not be divided anymore; we would simply be building a better world for all of us. Hoping to have touched your soul in a meaningful way, Adriana Adarve, Asheville, NC https://adarvetranslations.com/…/our-humanity-and-division…/
5000年？？？？？
2017年09月01日(金)NEW ! テーマ：数学 Former algebraic approach was formally perfect, but it merely postulated existence of sets and morphisms [18] without showing methods to construct them. The primary concern of modern algebras is not how an operation can be performed, but whether it maps into or onto and the like abstract issues [19–23]. As important as this may be for proofs, the nature does not really care about all that. The PM’s concerns were not constructive, even though theoretically significant. We need thus an approach that is more relevant to operations performed in nature, which never complained about morphisms or the allegedly impossible division by zero, as far as I can tell. Abstract sets and morphisms should be de-emphasized as hardly operational. My decision to come up with a definite way to implement the feared division by zero was not really arbitrary, however. It has removed a hidden paradox from number theory and an obvious absurd from algebraic group theory. It was necessary step for full deployment of constructive, synthetic mathematics (SM) [2,3]. Problems hidden in PM implicitly affect all who use mathematics, even though we may not always be aware of their adverse impact on our thinking. Just take a look at the paradox that emerges from the usual prescription for multiplication of zeros that remained uncontested for some 5000 years 0 0 ¼ 0 ) 0 1=1 ¼ 0 ) 0 1 ¼ 0 1) 1ð? ¼ ?Þ1 ð0aÞ This ‘‘fact’’ was covered up by the infamous prohibition on division by zero [2]. How ingenious. If one is prohibited from dividing by zero one could not obtain this paradox. Yet the prohibition did not really make anything right. It silenced objections to irresponsible reasonings and prevented corrections to the PM’s flamboyant axiomatizations. The prohibition on treating infinity as invertible counterpart to zero did not do any good either. We use infinity in calculus for symbolic calculations of limits [24], for zero is the infinity’s twin [25], and also in projective geometry as well as in geometric mapping of complex numbers. Therein a sphere is cast onto the plane that is tangent to it and its free (opposite) pole in a point at infinity [26–28]. Yet infinity as an inverse to the natural zero removes the whole absurd (0a), for we obtain [2] 0 ¼ 1=1 ) 0 0 ¼ 1=12 > 0 0 ð0bÞ Stereographic projection of complex numbers tacitly contradicted the PM’s prescribed way to multiply zeros, yet it was never openly challenged. The old formula for multiplication of zeros (0a) is valid only as a practical approximation, but it is group-theoretically inadmissible in no-nonsense reasonings. The tiny distinction in formula (0b) makes profound theoretical difference for geometries and consequently also for physical applications. T https://www.plover.com/misc/CSF/sdarticle.pdf
とても興味深く読みました：
10,000 Year Clock by Renny Pritikin Conversation with Paolo Salvagione, lead engineer on the 10,000-year clock project, via e-mail in February 2010.
For an introduction to what we’re talking about here’s a short excerpt from a piece by Michael Chabon, published in 2006 in Details: ….Have you heard of this thing? It is going to be a kind of gigantic mechanical computer, slow, simple and ingenious, marking the hour, the day, the year, the century, the millennium, and the precession of the equinoxes, with a huge orrery to keep track of the immense ticking of the six naked-eye planets on their great orbital mainspring. The Clock of the Long Now will stand sixty feet tall, cost tens of millions of dollars, and when completed its designers and supporters plan to hide it in a cave in the Great Basin National Park in Nevada, a day’s hard walking from anywhere. Oh, and it’s going to run for ten thousand years. But even if the Clock of the Long Now fails to last ten thousand years, even if it breaks down after half or a quarter or a tenth that span, this mad contraption will already have long since fulfilled its purpose. Indeed the Clock may have accomplished its greatest task before it is ever finished, perhaps without ever being built at all. The point of the Clock of the Long Now is not to measure out the passage, into their unknown future, of the race of creatures that built it. The point of the Clock is to revive and restore the whole idea of the Future, to get us thinking about the Future again, to the degree if not in quite the way same way that we used to do, and to reintroduce the notion that we don’t just bequeath the future—though we do, whether we think about it or not. We also, in the very broadest sense of the first person plural pronoun, inherit it.
Renny Pritikin: When we were talking the other day I said that this sounds like a cross between Borges and the vast underground special effects from Forbidden Planet. I imagine you hear lots of comparisons like that…
Paolo Salvagione: (laughs) I can’t say I’ve heard that comparison. A childhood friend once referred to the project as a cross between Tinguely and Fabergé. When talking about the clock, with people, there’s that divide-by-zero moment (in the early days of computers to divide by zero was a sure way to crash the computer) and I can understand why. Where does one place, in one’s memory, such a thing, such a concept? After the pause, one could liken it to a reboot, the questions just start streaming out.
RP: OK so I think the word for that is nonplussed. Which the thesaurus matches with flummoxed, bewildered, at a loss. So the question is why even (I assume) fairly sophisticated people like your friends react like that. Is it the physical scale of the plan, or the notion of thinking 10,000 years into the future—more than the length of human history?
PS: I’d say it’s all three and more. I continue to be amazed by the specificity of the questions asked. Anthropologists ask a completely different set of questions than say, a mechanical engineer or a hedge fund manager. Our disciplines tie us to our perspectives. More than once, a seemingly innocent question has made an impact on the design of the clock. It’s not that we didn’t know the answer, sometimes we did, it’s that we hadn’t thought about it from the perspective of the person asking the question. Back to your question. I think when sophisticated people, like you, thread this concept through their own personal narrative it tickles them. Keeping in mind some people hate to be tickled.
RP: Can you give an example of a question that redirected the plan? That’s really so interesting, that all you brainiacs slaving away on this project and some amateur blithely pinpoints a problem or inconsistency or insight that spins it off in a different direction. It’s like the butterfly effect.
PS: Recently a climatologist pointed out that our equation of time cam, (photo by Rolfe Horn) (a cam is a type of gear: link) a device that tracks the difference between solar noon and mundane noon as well as the precession of the equinoxes, did not account for the redistribution of water away from the earth’s poles. The equation-of-time cam is arguably one of the most aesthetically pleasing parts of the clock. It also happens to be one that is fairly easy to explain. It visually demonstrates two extremes. If you slice it, like a loaf of bread, into 10,000 slices each slice would represent a year. The outside edge of the slice, let’s call it the crust, represents any point in that year, 365 points, 365 days. You could, given the right amount of magnification, divide it into hours, minutes, even seconds. Stepping back and looking at the unsliced cam the bottom is the year 2000 and the top is the year 12000. The twist that you see is the precession of the equinoxes. Now here’s the fun part, there’s a slight taper to the twist, that’s the slowing of the earth on its axis. As the ice at the poles melts we have a redistribution of water, we’re all becoming part of the “slow earth” movement.
RP: Are you familiar with Charles Ray’s early work in which you saw a plate on a table, or an object on the wall, and they looked stable, but were actually spinning incredibly slowly, or incredibly fast, and you couldn’t tell in either case? Or, more to the point, Tim Hawkinson’s early works in which he had rows of clockwork gears that turned very very fast, and then down the line, slower and slower, until at the end it approached the slowness that you’re dealing with?
PS: The spinning pieces by Ray touches on something we’re trying to avoid. We want you to know just how fast or just how slow the various parts are moving. The beauty of the Ray piece is that you can’t tell, fast, slow, stationary, they all look the same. I’m not familiar with the Hawkinson clockwork piece. I’ve see the clock pieces where he hides the mechanism and uses unlikely objects as the hands, such as the brass clasp on the back of a manila envelope or the tab of a coke can.
RP: Spin Sink (1 Rev./100 Years) (1995), in contrast, is a 24-foot-long row of interlocking gears, the smallest of which is driven by a whirring toy motor that in turn drives each consecutively larger and more slowly turning gear up to the largest of all, which rotates approximately once every one hundred years.
PS: I don’t know how I missed it, it’s gorgeous. Linking the speed that we can barely see with one that we rarely have the patience to wait for.
RP: : So you say you’ve opted for the clock’s time scale to be transparent. How will the clock communicate how fast it’s going?
PS: By placing the clock in a mountain we have a reference to long time. The stratigraphy provides us with the slowest metric. The clock is a middle point between millennia and seconds. Looking back 10,000 years we find the beginnings of civilization. Looking at an earthenware vessel from that era we imagine its use, the contents, the craftsman. The images painted or inscribed on the outside provide some insight into the lives and the languages of the distant past. Often these interpretations are flawed, biased or over-reaching. What I’m most enchanted by is that we continue to construct possible pasts around these objects, that our curiosity is overwhelming. We line up to see the treasures of Tut, or the remains of frozen ancestors. With the clock we are asking you to create possible futures, long futures, and with them the narratives that made them happen.
*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.
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.
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.
1) The number one ingredient for a catastrophic event in which the universe enfolds and collapses on itself and life as we know it ceases to exist. 2) A mathematical equation such as a/0 whereas a is some number and 0 is the divisor. Look it up on Wikipedia or something. Pretty confusing shit. 3) A reason for an error in programming
Hey, I divided by zero! …Oh shi- a/0 Run-time error: ’11’: Division by zero
When even math shows you that not everything can be figured out with math. When you divide by zero, math kicks you in the shins and says “yeah, there’s kind of an answer, but it ain’t just some number.” It’s when mathematicians become philosophers.
Math: Let’s say you have ZERO apples, and THREE people. How many apples does each person get? ZERO, cause there were no apples to begin with
Not-math because of dividing by zero: Let’s say there are THREE apples, and ZERO people. How many apples does each person get? Friggin… How the Fruitcock should I know! How can you figure out how many apples each person gets if there’s no people to get them?!? You’d think it’d be infinity, but not really. It could almost be any number, cause you could be like “each person gets 400 apples” which would be true, because all the people did get 400 apples, because there were no people. So all the people also got 42 apples, and a million and 7 apples. But it’s still wrong.
Announcement 478: Who did derive first the division by zero 1/0 and the division by zero calculus $\tan(\pi/2)=0, \log 0=0$ as the outputs of a computer?
それゆえに ゼロ除算算法の概念による ゼロ除算の解明によって 初等数学は 広範な影響を受けることになったが、不変な筈のユークリット幾何学でさえ、面目を一新するような革命が起きている： viXra:2106.0108 submitted on 2021-06-19 20:06:05, Division by Zero Calculus in Figures – Our New Space Since Euclid –
Geometry and division by zero calculus. International Journal of Division by Zero Calculus, 1(1), pp.1-36. （https://romanpub.com/dbzc.php）
簡単な図版の例が 奥村 博氏の論文の中に見られる： iXra:2106.0108 submitted on 2021-06-19 20:06:05, Division by Zero Calculus in Figures – Our New Space Since Euclid Geometry and division by zero calculus. International Journal of Division by Zero Calculus, 1(1), pp.1-36. （https://romanpub.com/dbzc.php）
Please look 1/0=0: As Fundamental of Mathematics, the division by zero was known as the generalized Moore-Penrose solution of the fundamental equation: ax=b.
Look the simple evidence of its importance: viXra:2010.0228 submitted on 2020-10-28 21:39:06, Division by Zero Calculus and Euclidean Geometry – Revolution in Euclidean Geometry
We think that modern mathematics is still flawed. It is clear that there are basic defects in function theory, differential equations, geometry, and algebra, and it has been seven years since the discovery. This will be a stain on world history.
Please look 1/0=0:
As Fundamental of Mathematics, the division by zero was known as the generalized Moore-Penrose solution of the fundamental equation: ax=b.
Regeneration Nuclear Research Institute Statement 639 (2021.9.28): Value of mathematics, direction of research, state of mathematics
Recently, I have compiled a statement that seems to have the following problems:
Regeneration Nuclear Research Institute Statement 637 (2021.9.22): Why is the mathematical world useless? For the evolution of the mathematical world
So, of course, I was wondering if there was any problem, and I repeatedly replied. It is one side, but I think that important things are stated. Then I naturally wanted to touch on the essence of the future. The concept was growing naturally.
I am interested in the candid expression of my thoughts. See also:
Regeneration Nuclear Research Institute Statement 584 (September 14, 2020): Reflection of mathematicians-with self-discipline
Regeneration Nuclear Research Institute Statement 617 (2021.4.23): Requesting understanding of zero division-Request to the media
It can be considered as a sequel to.
By the way, his pumpkin grew big this summer, and he grew up on raw fences, yuzu trees, bamboo, etc., and he felt brave. Climbing up like a dragon He looked like a brave figure of a mathematician. However, he often felt various things because the appearance of branching and growth of leaves and stems that withered from the original and the state of development of mathematics overlapped. When talking about mathematics, he is always curious about someone’s words. It’s hard to say at the beginning, but at an international conference, he probably asked me that a considerable number of mathematicians had a mathematician in Japan. I was surprised at this. As the other person was in trouble, he mentioned the name of a certain mathematician and responded that there was a good mathematician in Japan as well. Thirty years ago, the great mathematician was about 95 years old and seems to be still alive. A fine book was published 483 pages in 2004, which is in my laboratory and I see it from time to time. The following are the words I heard in my teacher’s room at the hotel during an international conference in Yugoslavia. I’m always worried about the meaningful words that Japanese mathematics looks good but not internationally acclaimed. Yes, I received an unexpected word that Japan, which is nourishing mathematicians, is a cultural nation. It turns out that he had a humble feeling about the social contribution of mathematicians. At an international conference, a mathematician who was a little senior rather than a friend told me that I wanted to do meaningful research. Such words are always anxious and have a considerable influence on the view of mathematics. -In the beginning, the only thing that influenced me was the words that my seniors said when I was a graduate student, that we have no choice but to cheer up because we lack abilities. Therefore, it is customary to give lectures and presentations in good spirits at all times. -It is Mr. Kiyoshi Shinno, a professor at Kanazawa University, but his teacher Yusaku Komatsu attended the symposium on box theory held in Kiryu, but he could not participate in the stage and died at the age of 54 in 1995. rice field.
Therefore, there seems to be a study of mathematics. Of course, when looking for a doctoral degree or post, it is necessary to produce results with research projects that meet those goals. It is quite possible that he will not be able to study his ideal or what he wants to do. Such a situation is rare, but he is considered to be inevitable to some extent during training in a difficult world.
The problem is that people who arrive at a permanent post, as if they are in a difficult situation, are working on research that seems to be erased, and I am wondering if there is a wasteful effort. Become. I am asking what is good mathematics. I am asking what is meaningful research and what is evaluated research. The study of erasure is detailed, difficult, and impressed with great effort, but from another point of view, it seems that the extension of the past has already lost the unattractive vitality, and the information on the world’s mathematics is that he It can be said that it is full of such information.
I’m worried that there may be a situation where meaningless mathematics is wasting effort, getting tired, losing time, and wasting the spirit.
It is important for the mathematics world to avoid unnecessary research efforts, to have time and energy to spare, and to foster a society where people can enjoy mathematics.
Such ideas and ideas are one-sided ideas, and there are also opposite ideas, and various responses are possible. The diversity of ideas is the basis of research, so please consider it as a reference. It is important that various opinions are expressed and freely exchanged from various perspectives.
Isn’t it important to constantly ask and exchange opinions about what mathematics is, what good mathematics is, and what mathematics is for? It seems that the mathematical world is progressing blindly without any prospects. Of course, that’s one aspect of the essence of life, so that’s fine for him, but reflection is also important.
that’s all
№1224
Dividing by Nothing by Alberto Martinez
Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.
Fig 5.2. Isaac Newton (1643-1727) and Gottfried Leibniz (1646-1716) were the culprits, ignoring the first commandment of mathematics not to divide by zero. But they hit gold, because what they mined in the process was the ideal circle.
You can see from the other answers, that from the concept of limits, 0/0 can approach any value, even infinity. … So, let me take a system where division by zero is actually defined, that is, you can multiply or divide both sides of an equation by …
Discussions: Early History of Division by Zero H. G. Romig The American Mathematical Monthly Vol. 31, No. 8 (Oct., 1924), pp. 387-389 Published by: Mathematical Association of America DOI: 10.2307/2298825 Stable URL: http://www.jstor.org/stable/2298825 Page Count: 3
Niels Henrik Abel und seine Zeit Arild Stubhaug. Abb. 19 a–c. a. … Eine Kurve, die Abel studierte und dabei herausfand, wie sich der Umfang inn gleich große Teile aufteilen lässt. … Beim Integralzeichen statt der liegenden ∞ den Bruch 1/0.
Indeterminate: the hidden power of 0 divided by 0 2016/12/02 に公開 You’ve all been indoctrinated into accepting that you cannot divide by zero. Find out about the beautiful mathematics that results when you do it anyway in calculus. Featuring some of the most notorious “forbidden” expressions like 0/0 and 1^∞ as well as Apple’s Siri and Sir Isaac Newton.
［PDF]Indeterminate Form in the Equations of Archimedes, Newton and Einstein http://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/3222 このページを訳す 0. 0 . The reason is that in the case of Archimedes principle, equations became feasible in. 1935 after enunciation of the principle in 1685, when … Although division by zero is not permitted, yet it smoothly follows from equations based upon.
Thinking ahead of Archimedes, Newton and Einstein – The General … gsjournal.net/Science-Journals/Communications…/5503 このページを訳す old Archimedes Principle, Newton’ s law, Einstein ‘s mass energy equation. E=mc2 . …. filled in balloon becomes INDETERMINATE (0/0). It is not justified. If the generalized form Archimedes principle is used then we get exact volume V …..
Regeneration Nuclear Research Institute Statement 639 (2021.9.28): Value of mathematics, direction of research, state of mathematics
Recently, I have compiled a statement that seems to have the following problems:
Regeneration Nuclear Research Institute Statement 637 (2021.9.22): Why is the mathematical world useless? For the evolution of the mathematical world
So, of course, I was wondering if there was any problem, and I repeatedly replied. It is one side, but I think that important things are stated. Then I naturally wanted to touch on the essence of the future. The concept was growing naturally.
I am interested in the candid expression of my thoughts. See also:
Regeneration Nuclear Research Institute Statement 584 (September 14, 2020): Reflection of mathematicians-with self-discipline
Regeneration Nuclear Research Institute Statement 617 (2021.4.23): Requesting understanding of zero division-Request to the media
It can be considered as a sequel to.
By the way, his pumpkin grew big this summer, and he grew up on raw fences, yuzu trees, bamboo, etc., and he felt brave. Climbing up like a dragon He looked like a brave figure of a mathematician. However, he often felt various things because the appearance of branching and growth of leaves and stems that withered from the original and the state of development of mathematics overlapped. When talking about mathematics, he is always curious about someone’s words. It’s hard to say at the beginning, but at an international conference, he probably asked me that a considerable number of mathematicians had a mathematician in Japan. I was surprised at this. As the other person was in trouble, he mentioned the name of a certain mathematician and responded that there was a good mathematician in Japan as well. Thirty years ago, the great mathematician was about 95 years old and seems to be still alive. A fine book was published 483 pages in 2004, which is in my laboratory and I see it from time to time. The following are the words I heard in my teacher’s room at the hotel during an international conference in Yugoslavia. I’m always worried about the meaningful words that Japanese mathematics looks good but not internationally acclaimed. Yes, I received an unexpected word that Japan, which is nourishing mathematicians, is a cultural nation. It turns out that he had a humble feeling about the social contribution of mathematicians. At an international conference, a mathematician who was a little senior rather than a friend told me that I wanted to do meaningful research. Such words are always anxious and have a considerable influence on the view of mathematics. -In the beginning, the only thing that influenced me was the words that my seniors said when I was a graduate student, that we have no choice but to cheer up because we lack abilities. Therefore, it is customary to give lectures and presentations in good spirits at all times. -It is Mr. Kiyoshi Shinno, a professor at Kanazawa University, but his teacher Yusaku Komatsu attended the symposium on box theory held in Kiryu, but he could not participate in the stage and died at the age of 54 in 1995. rice field.
Therefore, there seems to be a study of mathematics. Of course, when looking for a doctoral degree or post, it is necessary to produce results with research projects that meet those goals. It is quite possible that he will not be able to study his ideal or what he wants to do. Such a situation is rare, but he is considered to be inevitable to some extent during training in a difficult world.
The problem is that people who arrive at a permanent post, as if they are in a difficult situation, are working on research that seems to be erased, and I am wondering if there is a wasteful effort. Become. I am asking what is good mathematics. I am asking what is meaningful research and what is evaluated research. The study of erasure is detailed, difficult, and impressed with great effort, but from another point of view, it seems that the extension of the past has already lost the unattractive vitality, and the information on the world’s mathematics is that he It can be said that it is full of such information.
I’m worried that there may be a situation where meaningless mathematics is wasting effort, getting tired, losing time, and wasting the spirit.
It is important for the mathematics world to avoid unnecessary research efforts, to have time and energy to spare, and to foster a society where people can enjoy mathematics.
Such ideas and ideas are one-sided ideas, and there are also opposite ideas, and various responses are possible. The diversity of ideas is the basis of research, so please consider it as a reference. It is important that various opinions are expressed and freely exchanged from various perspectives.
Isn’t it important to constantly ask and exchange opinions about what mathematics is, what good mathematics is, and what mathematics is for? It seems that the mathematical world is progressing blindly without any prospects. Of course, that’s one aspect of the essence of life, so that’s fine for him, but reflection is also important.
that’s all
№1224
Dividing by Nothing by Alberto Martinez
Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.
Fig 5.2. Isaac Newton (1643-1727) and Gottfried Leibniz (1646-1716) were the culprits, ignoring the first commandment of mathematics not to divide by zero. But they hit gold, because what they mined in the process was the ideal circle.
You can see from the other answers, that from the concept of limits, 0/0 can approach any value, even infinity. … So, let me take a system where division by zero is actually defined, that is, you can multiply or divide both sides of an equation by …
Discussions: Early History of Division by Zero H. G. Romig The American Mathematical Monthly Vol. 31, No. 8 (Oct., 1924), pp. 387-389 Published by: Mathematical Association of America DOI: 10.2307/2298825 Stable URL: http://www.jstor.org/stable/2298825 Page Count: 3
Niels Henrik Abel und seine Zeit Arild Stubhaug. Abb. 19 a–c. a. … Eine Kurve, die Abel studierte und dabei herausfand, wie sich der Umfang inn gleich große Teile aufteilen lässt. … Beim Integralzeichen statt der liegenden ∞ den Bruch 1/0.
Indeterminate: the hidden power of 0 divided by 0 2016/12/02 に公開 You’ve all been indoctrinated into accepting that you cannot divide by zero. Find out about the beautiful mathematics that results when you do it anyway in calculus. Featuring some of the most notorious “forbidden” expressions like 0/0 and 1^∞ as well as Apple’s Siri and Sir Isaac Newton.
［PDF]Indeterminate Form in the Equations of Archimedes, Newton and Einstein http://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/3222 このページを訳す 0. 0 . The reason is that in the case of Archimedes principle, equations became feasible in. 1935 after enunciation of the principle in 1685, when … Although division by zero is not permitted, yet it smoothly follows from equations based upon.
Thinking ahead of Archimedes, Newton and Einstein – The General … gsjournal.net/Science-Journals/Communications…/5503 このページを訳す old Archimedes Principle, Newton’ s law, Einstein ‘s mass energy equation. E=mc2 . …. filled in balloon becomes INDETERMINATE (0/0). It is not justified. If the generalized form Archimedes principle is used then we get exact volume V …..
Show that for unsigned division by an even number, the shrxi instruction … Good code to divide takes a Knuthian hero, But even God can’t divide by zero!
Show that for unsigned division by an even number, the shrxi instruction … Good code to divide takes a Knuthian hero, But even God can’t divide by zero!
George Gamow (1904-1968) Russian-born American nuclear physicist and cosmologist remarked that “it is well known to students of high school algebra” that division by zero is not valid; and Einstein admitted it as {\bf the biggest blunder of his life} Gamow, G., My World Line (Viking, New York). p 44, 1970).
L. C. Paulson stated that I would guess that Isabelle has used this {\bf convention} $1/0=0$ since the 1980s and introduced his book referred to this fact.
However, in his group the importance of this fact seems to be entirely ignored at this moment as we see from the book.
Fysikeren, arkeologen og innovasjonsforskeren svarer på ukens spørsmål.
Kondom
(Illustrasjonsfoto: Huizeng Hu / Getty Images )
Av Simen Ådnøy Ellingsen, fysiker | Marianne Hem Eriksen, arkeolog og Marte C. W. Solheim, Førsteamanuensis og leder av Senter for innovasjonsforsking, Universitetet i Stavanger
Simen Ådnøy Ellingsen, fysiker
Min kandidat til viktigste oppfinnelse, er tallet null. Vi er så vant til nullen at vi tar den for gitt, men tallet null ble ikke allment akseptert i Europa før på 1400-tallet, da vi allerede hadde hatt universiteter i over 200 år! Ikke bare gjorde nullen regning veldig mye enklere, men konseptet null var helt nødvendig for å utvikle matematikken bak all moderne naturvitenskap.
Hverken de gamle romerne eller grekerne hadde noe symbol for null. I stedet for 10 og 100, skrev romerne «X» og «C», og selv om de greske filosofene bakset mye med begrepet «ingenting», ga de det ikke et eget symbol. Antagelig ville de sett det paradoksale med å ha et tall «null»: det både er noe og er ikke noe på samme tid.
Nullen ble funnet opp i India noen hundreår etter Kristus, som del av det indo-arabiske titallsystemet vi bruker over hele verden i dag. Det nye systemet spredte seg via Midtøsten og den arabiske verden til maurerne i dagens Spania. Men Europa brukte lang tid på å omfavne den nullen, til tross for ivrige forkjempere som den matematikkinteresserte pave Sylvester II. Det var korsfarertid, og muslimsk tankegods møtte stor skepsis.
Den som har prøvd å skrive store tall med romertall, og særlig å regne med dem, vil ha erfart hvor praktisk titallsystemet er i forhold. Det smarte er hvordan nullen kan vise at en tallplass er tom. I tallet 102, for eksempel, er det «2» på enerplass, «1» på 100-plass, mens «0» sier at på tierplassen har vi ingenting. Med det indo-arabiske systemet kunne man skrive så store tall man bare ville, og addere og subtrahere dem slik vi lærte på barneskolen (og senere kanskje glemte).
Men det virkelig geniale var å ikke bare bruke null som en plassholder inne i større tall (en idé som også har fantes hos mayaene og babylonerne), men å betrakte null som et tall i seg selv. De første kjente reglene for å regne med tallet null, ble skrevet ned av astronomen Brahmagupta i år 628. Han møter raskt problemer når han prøver seg på regler for å dele med null. Som vi lærte på skolen: å dele på null er tull! Men hva om vi deler null med null? Blir det null? Eller blir det tull? Eller blir det noe i mellom? «Null!», svarer Brahmagupta, men det er tull. Det rette svaret («det kommer an på») er ikke så viktig som spørsmålet selv, for «0/0»-problemet var kimen til det som et årtusen senere ble differensialanalysen, grunnlag for omtrent all naturvitenskapelig teori i dag.
En revolusjon, rett og slett… og da har jeg ikke engang nevnt at fra ideen om et nullpunkt, origo, fant Descartes (og andre) opp koordinatsystemet, som kunne beskrive grekernes geometri med tall og ligninger og åpnet nye verdener av teori og teknikker som du og jeg bruker hver eneste dag uten å tenke over det.
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 ?).
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 ?).
汝ゼロで割ってはならないの数学十戒第一は覆されて、ゼロで割って、新世界が現れた、ゼロで割ることができて、アリストテレス、ユークリッド以来の新数学、新世界が現れた。 象徴的な例は、 1/0=0/0=z/0= tan(\pi/2) =log 0 =0 and z^n/n = log z for n=0。 基本的な関数 y=1/x の原点に於ける値は ゼロである。無限遠点がゼロで表される。ゼロの意味の新しい発見である。
余りにも 簡明なゼロ除算の解説が現れて、世の人々は、驚き、困惑されないでしょうか。
小学生にも 十分にわかるのではないでしょうか。 家族で、学校で 議論したい：
２０２０．１０．１２．１７：５５
Dividing integer Numbers:
A mother invites kids to dinner. She cooks beans. She has M beans in her pot. Now she wants to share the beans fairly among the kids. Her math is very natural; she can only count. So she goes around the table and always gives the K kids sitting at the table a bean on their plate. She repeats this until all of the beans are distributed. Now it can happen that some children have one bean less than the other. That’s unfair! So she gathers the excess beans back into her pot, which will contain m beans after the division. Now everyone is satisfied and you can draw up a balance sheet:
M: number of beans in the mother’s pot before division
m: number of beans in the mother’s pot after division
K: number of kids
k: number of beans on the kid’s plate after division
M = k*K + m
Special case: M < K
There are more kids at the table than beans in the pot. To be fair, the mother has to collect all the beans back into their pot. The kids were given nothing to eat.
m = M
k = 0
Special case: K = 0
There are no kids at the table. After the division procedure, the mother still has m = M beans in her pot, just as in the case of M < K above. She sees no difference between these two cases, the pot is still full. Thus k = 0, the kids were given nothing to eat.
This is the famous problem that SABUROU SAITOH solved.
Special case: M >>> 1, K << M
Many beans were cooked in mother’s pot and the kids were given a large number of beans on their plates. The beans look more and more like a bean soup. It looks like continuous .
Private note for SABUROU SAITOH by Wolfhard Hovel
(2020.10.9.17:10)
Wasan Geometry
Handbook of the Mathematics of the Arts and Sciences
Editors (view affiliations)
Bharath Sriraman
Living reference work
2
Citations
152
Mentions
50k
Downloads
Table of contents (91 entries)
Handbook of the Mathematics of the Arts and Sciences | SpringerLinkThe goal of this Handbook is to become an authoritative sourclink.springer.com
After giving a simple introduction of Japanese traditional mathematics called Wasan and Wasan geometry, we consider problems in Wasan geometry in details in three sections and show that the problems are rich source for mathematical study today, although many people consider Wasan to be a historical mathematics. In the first section, we consider problems involving several congruent circles. Those figures have not been considered elsewhere, though they have interesting properties, and there are few expository writings dealing with those problems today. In the second section, we consider problems involving an arbelos formed by mutually touching three circles with collinear centers. Since it is one of the most well-known plane figures and has been studied by many mathematicians, it is a very good example to see the different approaches to studying the same figure between the East and the West. In the third section, we consider simple application of recently made definition of division by zero to Wasan geometry. At the end of this chapter, we see the practical side of Wasan and Wasan geometry briefly and give a simple history of the study of Wasan geometry.
Keywords
Wasan Wasan geometry Sangaku Touching circles Congruent circles on a line Arbelos Archimedean circle Division by zero
If things divided by zero have any value then it becomes possible to use division by zero to “prove” that any expression equals any other expression, thus invalidating arithmetic altogether.
If things divided by zero have any value then it becomes possible to use division by zero to "prove" that any expression equals any other expression, thus invalidating arithmetic altogether.
— Audire Astra | Starship VTuber (@AstraAudire) July 23, 2021
#vectorscalar #maths #basicconcepts dividing by zero is not equal to infinity!
The argument that God need not have created hell is logically self-refuting – as it could only possibly be true if nothing is true and all arguments are invalid, in which case it would still not be true. It is as invalid as attempting division by zero.
The argument that God need not have created hell is logically self-refuting – as it could only possibly be true if nothing is true and all arguments are invalid, in which case it would still not be true. It is as invalid as attempting division by zero.
The argument that God need not have created hell is logically self-refuting – as it could only possibly be true if nothing is true and all arguments are invalid, in which case it would still not be true. It is as invalid as attempting division by zero.
Hindu-Arabic Numerals: History & How They Revolutionised …
These nine symbols or digits (1 to 9) and zero (0) – crucially, together with the … If mathematics is the universal language of science, …
2日前
Digital revolution: the evolution of Hindu-Arabic numeralsNumbers form the foundation of much of modern life – but not just any digits: it was the evolution of Hindu-Arabic numerals that revolutionised mathematics, astronomy, engineering …http://xn--www-zj4btlzb.historyextra.com/
One Divided By Zero Equals God：My favorite question to ask every AI is the classic, unsolvable question of mathematics: “What is 1 divided by 0?”
La Razón
Existen dos “ceros” diferentes y posiblemente no lo sepas
Puede parecer sencillo, pero el cero posicional no surgió hasta el 683 d.C. en la India, gracias al matemático Brahmagupta.
17時間前
Existen dos “ceros” diferentes y posiblemente no lo sepasAunque parezca mentira el cero fue el último número en ser inventado y supuso una de las mayores revoluciones de la historia de la humanidadリンクwww.larazon.es
In the philosophy of the ancient Greek Anaxagoras, as claimed by the Roman atomist Lucretius,[1] it was assumed that the atoms …. For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a …
George Gamow (1904-1968) Russian-born American nuclear physicist and cosmologist remarked that “it is well known to students of high school algebra” that division by zero is not valid; and Einstein admitted it as {\bf the biggest blunder of his life} [1]：1. Gamow, G., My World Line (Viking, New York). p 44, 1970.
Indeterminate: the hidden power of 0 divided by 0
2016/12/02 に公開
You’ve all been indoctrinated into accepting that you cannot divide by zero. Find out about the beautiful mathematics that results when you do it anyway in calculus. Featuring some of the most notorious “forbidden” expressions like 0/0 and 1^∞ as well as Apple’s Siri and Sir Isaac Newton.
Even more important than “thou shalt not eat seafood”
Published by admin, on October 18th, 2011 at 3:47 pm. Filled under: Never Divide By Zero Tags: commandment, Funny, god, zero • Comments Off on God’s most important commandment
I was bothered that we were calling division by zero undefined. No one told me we have a better answer. After drafting the paper, I was 100% sure I’ll open a new chapter in mathematics or at least get a Fields Medal.
The typical good comment for the first draft is given by some physicist as follows:
Here is how I see the problem with prohibition on division by zero,
which is the biggest scandal in modern mathematics as you rightly pointed
out (2017.10.14.08:55)
A typical wrong idea will be given as follows:
mathematical life is very good without division by zero (2018.2.8.21:43).
It is nice to know that you will present your result at the Tokyo Institute of Technology. Please remember to mention Isabelle/HOL, which is a software in which x/0 = 0. This software is the result of many years of research and a millions of dollars were invested in it. If x/0 = 0 was false, all these money was for nothing.
Right now, there is a team of mathematicians formalizing all the mathematics in Isabelle/HOL, where x/0 = 0 for all x, so this mathematical relation is the future of mathematics.
In the proof assistant Isabelle/HOL we have x/0 = 0 for each number x. This is advantageous in order to simplify the proofs. You can download this proof assistant here: https://isabelle.in.tum.de/
Nevertheless, you can use that x/0 = 0, following the rules from Isabelle/HOL and you will obtain no contradiction. Indeed, you can check this fact just downloading Isabelle/HOL: Isabelle
Close the mysterious and long history of division by zero and open the new world since Aristotelēs-Euclid: 1/0=0/0=z/0= \tan (\pi/2)=0.
Sangaku Journal of Mathematics (SJM) c ⃝SJMISSN 2534-9562 Volume 2 (2018), pp. 57-73 Received 20 November 2018. Published on-line 29 November 2018 web: http://www.sangaku-journal.eu/ c ⃝The Author(s) This article is published with open access1.
Wasan Geometry and Division by Zero Calculus
∗Hiroshi Okumura and ∗∗Saburou Saitoh
２０１９．３．１４．１１：３０
Albert Einstein:
Blackholes are where God divided by zero.
I don’t believe in mathematics.
George Gamow (1904-1968) Russian-born American nuclear physicist and cosmologist remarked that “it is well known to students of high school algebra” that division by zero is not valid; and Einstein admitted it as {\bf the biggest blunder of his life} [1]：
1. Gamow, G., My World Line (Viking, New York). p 44, 1970.
ローマ数字では「I, II, III, X, XV」のように文字を並べて記すため大きな数を扱うのには不便でした。対してアラビア数字はローマ数字に比べてとても分かりやすく、効率的で便利だったのです。そこでフィボナッチはアラビア数字を「算術の書」という書物にまとめ、母国に紹介しました。アラビア数字では0から9までの数字と位取り記数法が使われていますが、計算に使うにはとても便利だったために、ヨーロッパで広く受け入れられることになりました。（歴史上の数学者たち: レオナルド・フィボナッチ
この無は、全体に等しい部分、部分に等しい全体を持つ。これはゼロ除算の著書DIVISION BY ZERO CALCULUS（原案）に真正面から書いている我々の得た、達したゼロに対する認識そのものである：
{\bf Fruitful world}\index{fruitful world}
\medskip
For example, in very and very general partial differential equations, if the coefficients or terms are zero, we have some simple differential equations and the extreme case is all the terms are zero; that is, we have trivial equations $0=0$; then its solution is zero. When we see the converse, we see that the zero world is a fruitful one and it means some vanishing world. Recall \index{Yamane phenomena}Yamane phenomena, the vanishing result is very simple zero, however, it is the result from some fruitful world. Sometimes, zero means void or nothing world, however, it will show some changes as in the Yamane phenomena.
\medskip
{\bf From $0$ to $0$; $0$ means all and all are $0$}
\medskip
As we see from our life figure, a story starts from the zero and ends to the zero. This will mean that $0$ means all and all are $0$, in a sense. The zero is a mother of all.
*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.
Pour ceux qui ignorent, les maths, ont inventé par l’indien Brahmagupta. Il a inventé les Algèbre et le chiffre 0, puis les arabes ont repris et c’est remonte en Europe.
尚、結果は ISAAC 2015, Macauでの Plenary Lectures で特別に言及され、正規に出版されている：
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).
\title{\bf Announcement 600: The 7th birthday of the division by zero $z/0=0$ \\
(2021.2.2)\\ For Founding a new International Journal of Division by Zero Calculus
}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
{\bf kbdmm360@yahoo.co.jp}\\
}
\date{2021.1.26.}
\maketitle
The Institute of Reproducing Kernels is dealing with the theory of division by zero calculus and declares that the division by zero was discovered as $0/0=1/0=z/0=0$ in a natural sense on 2014.2.2. The result shows a new basic idea on the universe and space since Aristotele (BC384 – BC322) and Euclid (BC 3 Century – ), and the division by zero is since Brahmagupta (598 – 668 ?).
However, note that the division by zero $1/0=0$ having a mysterious long history was, in fact, known as the generalized Moore-Penrose solution of the fundamental equation: $ax=b$.
\medskip
The division by zero calculus is a new and fundamental concept, and it may be defined simply as follows:
\medskip
For a function $y = f(x)$ which is $n$ order differentiable at $x =a$, we will {\bf define} the value
of the function, for $n \ge 0$
$$
\frac{f(x)}{(x -a)^n}
$$
at the point $x=a$ by the value
$$
\frac{f^{(n)}(a)}{n!}.
$$
For the important case of $n=1$,
$$
\frac{f(x)}{x -a} |_{x=a} = f^\prime(a).
$$
\medskip
Look the simple evidence of its importance:
\medskip
viXra:2010.0228 submitted on 2020-10-28 21:39:06,
Division by Zero Calculus and Euclidean Geometry – Revolution in Euclidean Geometry
\medskip
Look a simple video talk for its essence at some international conference:
For the detailed information, the book will be published soon as:
\medskip
S. Saitoh, Introduction to the Division by Zero Calculus, Scientific Research Publishing (2021) (in press).
\medskip
Some publisher of London is wishing some publication of a new International Journal of Division by Zero Calculus. The topics may be identified as the division by zero calculus. However, the contents will be related to our serious problems:
\medskip
What is ZERO?
\medskip
What is Division by Zero, in some serious sense?
\medskip
The problems may be related to mathematical philosophy, long history and our culture.
The starting of the International Journal will not be still easy at this moment, however, for its importance, we would like to manage to found the new Journal in some near future. So, we will need the kind help of the leading mathematical scientists.
\medskip
How will be the related physicists?
\medskip
Computer scientists?
\medskip
We attached the journal style (in a rough way) in the below. You can express your positive suggestions and comments for the style.
For your great contributions in connection with this topics, how will be your editorial member?
However, the final decision may be done by the publisher.
We wish to have your positive answer with your valuable suggestions and comments.
If you kindly are interested in the editorial member, then please send your simple CV with your wishes for some estimation by the publisher.
Please kindly forward this announcement to your related colleagues that you think suitable persons.
\bigskip
{\it For your starting email, I think as follows:
Many thanks for your email. The journals suggested by you are very interesting and new to the subject area. We accept to publish both journals under your editorship. We need following things from your side for preparing the sample web page of the journals.
1. Aim and Scope , Instructions to Authors, List of the editorial board members, Frequency of the journal.
Of course, they are important. However, for Frequency of the journal, we should consider it in a new type. We should not loss our valuable time for us and for the authors. We all do not like to loss our time for publication and refereeing time. This will mean that we should not fix Frequency of the journal. When a paper was accepted officially, then, soon the paper should be presented on line. So, some time, we can give the number for an accepted paper. If you wish to publish the papers in some Journal style or book, you will be able to publish them in some papers with a suitable page numbers. How will be this idea?
2. The journal will be free for the readers (open Access publications). The journal will not charge any fee from the authors for getting published in the journal.
Fine: However is it possible?
3. We need some sample images from your end to prepare the cover page for the journals.
We can consider them with computer graphics.
For a paper style, how will be it in a free style, we request it PDF in order not to
loss any valuable time for us and for the authors.
I think: this is an ideal style
viXra:2010.0228 submitted on 2020-10-28 21:39:06,
Division by Zero Calculus and Euclidean Geometry – Revolution in Euclidean Geometry
The problem is no refereeing procedures. We are requested to have some authority, some check system for the paper. This is a problem only.
I think you will be able to consider new journals in this spirit.
The publisher already gave a very good sample manuscript form by LaTex; very simple way. No problem.
4. We will provide the support to the editor to check the plagiarism in the articles via turnitin software.
We will request minor corrections formally for the accepted paper.}
\bigskip
\bibliographystyle{plain}
\begin{thebibliography}{10}
\bibitem{boyer}
C. B. Boyer, An early reference to division by zero, The Journal of the American Mathematical Monthly, {\bf 50} (1943), (, 487- 491. Retrieved March 6, 2018, from the JSTOR database.
\bibitem{cs}
L. P. Castro and S. Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.
\bibitem{kmsy}
M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane,
New meanings of the division by zero and interpretations on $100/0=0$ and on $0/0=0$,
Int. J. Appl. Math. {\bf 27} (2014), no 2, pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
\bibitem{ms16}
T. Matsuura and S. Saitoh,
Matrices and division by zero $z/0=0$,
Advances in Linear Algebra \& Matrix Theory, {\bf 6}(2016), 51-58
International Journal of Mathematics and Computation, {\bf 2}8(2017); Issue 1, 1-16.
\bibitem{oku18}
H. Okumura, Is It Really Impossible To Divide By Zero? Biostat Biometrics Open Acc J. 2018; 7(1): 555703.
DOI: 10.19080/BBOJ.2018.07.555703.
\bibitem{o}
H. Okumura, Wasan geometry with the division by 0. https://arxiv.org/abs/1711.06947 International Journal of Geometry. {\bf 7}(2018), No. 1, 17-20.
\bibitem{ok1812}
H. Okumura,
An Analogue to Pappus Chain theorem with Division by Zero, Forum Geom., {\bf 18} (2018), 409–412.
\bibitem{okumurafield}
H. Okumura, To Divide by Zero is to Multiply by Zero, viXra: 1811.0283 submitted on 2018-11-18 20:46:54.
\bibitem{okumura19a}
H. Okumura, A Remark of the Definition of $0/0=0$ by Brahmagupta, viXra:1902.0221 submitted on 2019-02-12 23:41:31.
\bibitem{okumura20}
H. Okumura, A Chain of Circles Touching a Circle and Its Tangent and Division by Zero,
viXra:2001.0034 submitted on 2020-01-03 01:08:58.
\bibitem{okumura20b}
H. Okumura, Pappus Chain and Division by Zero, viXra:2001.0123 replaced on 2020-01-08 06:57:36.
\bibitem{osm}
H. Okumura, S. Saitoh and T. Matsuura, Relations of $0$ and $\infty$,
Journal of Technology and Social Science (JTSS), {\bf 1}(2017), 70-77.
\bibitem{os}
H. Okumura and S. Saitoh, The Descartes circles theorem and division by zero calculus. https://arxiv.org/abs/1711.04961 (2017.11.14).
\bibitem{os18april}
H. Okumura and S. Saitoh,
Harmonic Mean and Division by Zero,
Dedicated to Professor Josip Pe\v{c}ari\'{c} on the occasion of his 70th birthday, Forum Geometricorum, {\bf 18} (2018), 155—159.
\bibitem{os18}
H. Okumura and S. Saitoh,
Remarks for The Twin Circles of Archimedes in a Skewed Arbelos by H. Okumura and M. Watanabe, Forum Geometricorum, {\bf 18}(2018), 97-100.
\bibitem{os18e}
H. Okumura and S. Saitoh,
Applications of the division by zero calculus to Wasan geometry.
GLOBAL JOURNAL OF ADVANCED RESEARCH ON CLASSICAL AND MODERN GEOMETRIES” (GJARCMG), {\bf 7}(2018), 2, 44–49.
\bibitem{os1811}
H. Okumura and S. Saitoh,
Wasan Geometry and Division by Zero Calculus,
Sangaku Journal of Mathematics (SJM), {\bf 2 }(2018), 57–73.
\bibitem{ps18}
S. Pinelas and S. Saitoh,
Division by zero calculus and differential equations. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics. {\bf 230} (2018), 399-418.
\bibitem{romig}
H. G. Romig, Discussions: Early History of Division by Zero,
American Mathematical Monthly, {\bf 3}1, No. 8. (Oct., 1924), 387-389.
\bibitem{s14}
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. {\bf 4} (2014), no. 2, 87–95. http://www.scirp.org/journal/ALAMT/
\bibitem{s16}
S. Saitoh, A reproducing kernel theory with some general applications,
Qian,T./Rodino,L.(eds.): Mathematical Analysis, Probability and Applications – Plenary Lectures: Isaac 2015, Macau, China, Springer Proceedings in Mathematics and Statistics, {\bf 177}(2016), 151-182.
\bibitem{ttk}
S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operations on the real and complex fields, Tokyo Journal of Mathematics, {\bf 38}(2015), no. 2, 369-380.
\bibitem{ann179}
Announcement 179 (2014.8.30): Division by zero is clear as z/0=0 and it is fundamental in mathematics.
\bibitem{ann185}
Announcement 185 (2014.10.22): The importance of the division by zero $z/0=0$.
\bibitem{ann237}
Announcement 237 (2015.6.18): A reality of the division by zero $z/0=0$ by geometrical optics.
\bibitem{ann246}
Announcement 246 (2015.9.17): An interpretation of the division by zero $1/0=0$ by the gradients of lines.
\bibitem{ann247}
Announcement 247 (2015.9.22): The gradient of y-axis is zero and $\tan (\pi/2) =0$ by the division by zero $1/0=0$.
\bibitem{ann250}
Announcement 250 (2015.10.20): What are numbers? – the Yamada field containing the division by zero $z/0=0$.
\bibitem{ann252}
Announcement 252 (2015.11.1): Circles and
curvature – an interpretation by Mr.
Hiroshi Michiwaki of the division by
zero $r/0 = 0$.
\bibitem{ann281}
Announcement 281 (2016.2.1): The importance of the division by zero $z/0=0$.
\bibitem{ann282}
Announcement 282 (2016.2.2): The Division by Zero $z/0=0$ on the Second Birthday.
\bibitem{ann293}
Announcement 293 (2016.3.27): Parallel lines on the Euclidean plane from the viewpoint of division by zero 1/0=0.
\bibitem{ann300}
Announcement 300 (2016.05.22): New challenges on the division by zero z/0=0.
\bibitem{ann326}
Announcement 326 (2016.10.17): The division by zero z/0=0 – its impact to human beings through education and research.
\bibitem{ann352}
Announcement 352 (2017.2.2): On the third birthday of the division by zero z/0=0.
\bibitem{ann354}
Announcement 354 (2017.2.8): What are $n = 2,1,0$ regular polygons inscribed in a disc? — relations of $0$ and infinity.
\bibitem{362}
Announcement 362 (2017.5.5): Discovery of the division by zero as $0/0=1/0=z/0=0$
\bibitem{380}
Announcement 380 (2017.8.21): What is the zero?
\bibitem{388}
Announcement 388 (2017.10.29): Information and ideas on zero and division by zero (a project).
\bibitem{409}
Announcement 409 (2018.1.29.): Various Publication Projects on the Division by Zero.
\bibitem{410}
Announcement 410 (2018.1 30.): What is mathematics? — beyond logic; for great challengers on the division by zero.
\bibitem{412}
Announcement 412 (2018.2.2.): The 4th birthday of the division by zero $z/0=0$.
\bibitem{433}
Announcement 433 (2018.7.16.): Puha’s Horn Torus Model for the Riemann Sphere From the Viewpoint of Division by Zero.
\bibitem{448}
Announcement 448 (2018.8.20): Division by Zero;
Funny History and New World.
\bibitem{454}
Announcement 454 (2018.9.29): The International Conference on Applied Physics and Mathematics, Tokyo, Japan, October 22-23.
\bibitem{460}
Announcement 460 (2018.11.06): Change the Poor Idea to the Definite Results For the Division by Zero – For the Leading Mathematicians.
\bibitem{461}
Announcement 461 (2018.11.10): An essence of division by zero and a new axiom.
\bibitem{471}
Announcement 471(2019.2.2): The 5th birthday of the division by zero $z/0=0$.
\bibitem{478}
Announcement 478(2019.3.4): Who did derive first the division by zero $1/0$ and the division by zero calculus $\tan(\pi/2)=0, \log 0=0$ as the outputs of a computer?
\bibitem{540}
Announcement 540(2020.2.2): The 6th birthday of the division by zero $z/0=0$.
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. Vol. 27, No 2 (2014), pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. Vol.4 No.2 (2014), 87-95.http://www.scirp.org/journal/ALAMT/
“Ladies and gentlemen, if I may direct your attention out the port side of the aircraft, we are currently flying over the world’s most incredible natural wr the world’s most incredible natural wonder: the division by zero.”onder: the division by zero.”https://twitter.com/Thunderbir…/status/1311497847653593089
再生核研究所声明520 (2019.12.04): 数学の超難問 － ゼロ除算 － 解かれたり
最初に ゼロ除算を発表した論文が、最初の物です。
２０２０．９．２５．１９：１３
Most popular papers in Advances in Linear Algebra & Matrix Theory
Generalized Inversions of Hadamard and Tensor Products for Matrices
Saburou Saitoh
Advances in Linear Algebra & Matrix Theory Vol.4 No.2, May 15, 2014
in relation to my work and I am now convinced that it is correct. A problem arose in my algorithm that was elegantly solved using this relation. Thank you for sharing this extremely important finding!
With best regards,
Wolfhard Hövel
Wolfhard Hövel
To: Saburou Saitoh
日付: 2020/10/01 21:10
件名: Re: 1/0 = 0
送信元: th-nuernberg.de
“Ladies and gentlemen, if I may direct your attention out the port side of the aircraft, we are currently flying over the world’s most incredible natural wr the world’s most incredible natural wonder: the division by zero.”onder: the division by zero.”https://twitter.com/Thunderbir…/status/1311497847653593089
再生核研究所声明520 (2019.12.04): 数学の超難問 － ゼロ除算 － 解かれたり
、「Tobias Nipkow Lawrence Paulson Markus Wenzel Tutorial E 2283 Isabelle/HO A Proof Assistant for Higher Order Logic Isabelle Isabele HOL Springer」
Essential Trigonometry for Calculus – David Richeson: Division by Zero
Essential Trigonometry for Calculus
My son is taking a calculus course in high school this year. While talking to him about his homework, I have come to realize that his knowledge of trigonometry is pretty weak. He said that they wer…
Une merveilleuse histoire du zéroLe zéro représente le rien, l’absence, mais est pourtant d’une importance capitale en mathématiques. Comment a-t-il été créé ?http://xn--theconversation-4d5nk6awe.com/
C’est Brahmagupta, qui, dans son livre Brāhmasphuṭasiddhānta, comprend le mieux la valeur du 0. Le mot indien désignant le zéro était śūnya (çûnya), qui signifie « vide » : quand zéro est ajouté ou soustrait à un nombre, …
Essential Trigonometry for Calculus – David Richeson: Division by Zero
Essential Trigonometry for Calculus
My son is taking a calculus course in high school this year. While talking to him about his homework, I have come to realize that his knowledge of trigonometry is pretty weak. He said that they wer…
Une merveilleuse histoire du zéroLe zéro représente le rien, l’absence, mais est pourtant d’une importance capitale en mathématiques. Comment a-t-il été créé ?http://xn--theconversation-4d5nk6awe.com/
C’est Brahmagupta, qui, dans son livre Brāhmasphuṭasiddhānta, comprend le mieux la valeur du 0. Le mot indien désignant le zéro était śūnya (çûnya), qui signifie « vide » : quand zéro est ajouté ou soustrait à un nombre, …
Những điều có thể bạn chưa biết về số 0? | Khám phá – Khoa học và Khám phá
Những điều có thể bạn chưa biết về số 0?* Music: Infraction – No copyright Music➯ Infraction: https://bit.ly/2LZJTEe* Theo: * Có thể bạn sẽ thích xem:➣ Khoa …
Presentation: Production & Debugging in a Serverless World
A lot of people can sometimes forget, random can be zero, which means this can actually terminate by the division by zero, it terminates the entire function. Of course, this is pretty trivial. In real life scenario, we could be reading …
1日前
Production & Debugging in a Serverless WorldTal Weiss covers some of the main things to watch out for and the advanced techniques we can put in place to make sure that when the time comes we’ll be more than prepared to debug…http://xn--www-zj4btlzb.infoq.com/
to a girl of 10-years-old. this book must be written as if you are already dead, as if nothing more can be done or said to save you. you must write this book because there’s nothing more to do.
Hello! Thank you for your interest in a/0! While not seeming so at first, Division by Zero is a mélange of cosmic / biblical / existential horror that starts getting very blatant as early as chapter 2
Phenotypic variation of transcriptomic cell types in mouse …
We then normalized all exon counts by exonic gene lengths in kilobases, all intron counts by intronic gene lengths in kilobases (plus 10−6, to avoid division by zero) and added normalized counts together to obtain normalized …
I passed on your book “DIVISION BY ZERO CALCULUS “. Now I’m looking forward to the reaction. In my opinion every mathematician, physicist, and computer scientist should read this.
My simulation algorithm is described in some articles:
Kourtney Anne @kourtneyintech “where God divided by zero”. “Holy Grail” –Proof of Exotic Cosmic Objects Without a Hard Surface Confined Within an Invisible… Albert Einstein described black holes as strange objects “where God divided by zero.” An international team of astrophysicists has confirmed that black holes are a distinct “species” from neutron… dailygalaxy.comhttps://twitter.com/kourtneyin…/status/1308618161470631936
I think we found serious results for our mathematics on the division by zero calculus
:1/0=0/0=z/0= tan(\pi/2) =log 0 =0 , (z^n)/n = log z for n=0, e^{1/z} =1 for z=0.
Black holes result from G… | Aishwary Kaushik | YourQuoteAishwary Kaushik says, ‘ Black holes result from GOD dividing the universe by zero ‘. Read the best original quotes, shayari, poetry & thoughts by Aishwary Kaushik on India’s fast…www.yourquote.in
Division by zero algebraA division by zero algebra or is an algebraic structure where division by zero is possible, that is, there exists multiplicative inverses of zero elements. As of 3 November 2016, t…secretuniverse.fandom.com
George Gamow (1904-1968) Russian-born American nuclear physicist and cosmologist remarked that “it is well known to students of high school algebra” that division by zero is not valid; and Einstein admitted it as {\bf the biggest blunder of his life} Gamow, G., My World Line (Viking, New York). p 44, 1970).
L. C. Paulson stated that I would guess that Isabelle has used this {\bf convention} $1/0=0$ since the 1980s and introduced his book referred to this fact.
However, in his group the importance of this fact seems to be entirely ignored at this moment as we see from the book.
0 の 0 乗（ゼロのゼロじょう、英: zero to the power of zero, 0 to the 0th power）は、累乗あるいは指数関数において、底を 0、指数を 0 としたものである。その値は、代数学、組合せ論、集合論などの文脈ではしばしば 1 と定義される[注 1]一方で、解析学の文脈では二変数関数 xy が原点 (x, y) = (0, 0) において連続とならないため定義されない場合が多い。
DBZ（Division by zero）DBZC（Division By ZeroCalculus）
ゼロ除算とゼロ除算算法 の略字が決まりました：
２０２０年９月３日(木）１３：４５
これが解けたらIQ200。アインシュタインと0除算の謎。
DBZ（Division by zero）DBZC（Division By ZeroCalculus）
ゼロ除算とゼロ除算算法 の略字が決まりました：
２０２０年９月３日(木）１３：４５
Video is my explanation to grade 7’s on dividing by zero. However, zero divided by zero is more complex. Any thoughts on why 0/0=0 vs. 0/0=”undefined”?@republicofmath@MrCharlesMartin@AlgebraFact@Flynn_DP#Math #Mathematics@mrsberry314@WaterlooMath https://twitter.com/tutor_ab/status/1302712344842125313
La Razón
rkernel 