Four Step Recovery Programme for Division by Zero Deniers

[@transmathematica]

If you believe division by zero is impossible, leave a comment below to say why, along with a link to any evidence to back up your belief. I will either reply or make a video to show you how, despite your beliefs, it is possible to divide by zero. I hope this will lead to a deeper understanding.

[@saburousaitoh]

0/0=0 was known in India 1300 years ago: Please look 1/0=0: As Fundamental of Mathematics, the division by zero was known as the generalized Moore-Penrose solution of the fundamental equation: ax=b. Look the simple evidence of its importance: viXra:2010.0228 submitted on 2020-10-28 21:39:06, Division by Zero Calculus and Euclidean Geometry - Revolution in Euclidean Geometry Look a simple video talk for its essence at some international conference: media.cmd.gunma-u.ac.jp/media/Play/ef7ca967c3fd4dabb188128fd6038cb81d Book was published: INTRODUCTION TO THE DIVISION BY ZERO CALCULUS SABUROU SAITOH January, 2021 www.scirp.org/book/DetailedInforOfABook.aspx?bookID=2746 www.amazon.com/dp/1649970889?ref=myi_title_dp books.google.com.ua/books/about?id=BnkZEAAAQBAJ&redir_esc=y play.google.com/store/books/details?id=BnkZEAAAQBAJ plaza.rakuten.co.jp/reproducingkerne/ New Journal on DBZC: （romanpub.com/dbzc.php） romanpub.com/dbzc.php

[@timpani112]

There is a missing piece to this presentation. What do you mean when you say that you divide by zero? Is there any application to this besides error-handling? As I think you are aware of, most people understand division as an operation that negates multiplication, i.e., division is the tool we use when we try to answer questions like "I had a number x, and when I multiplied x by 5 I got 10. What was my original number x?" If we replace 5 by 0 in the above question, then 10 is also replaced by 0 and there is no way to answer the question. The number 0 is unique among the real numbers in this regard, as it is the only absorbing element among the real numbers. So what do we gain by defining an operation that we call "division" which includes the number 0? Can you give an example of a mathematical problem that can be solved using division by 0, and how it's actually done? Right now it's difficult for me to think of a single mathematical application of this, but I see in the wiki article about you that you have made some pretty strong claims about how this could solve some rather difficult problems. Maybe include some explanation of those in the next video?

[@transmathematica]

timpani112, Many thanks for your questions. I am sure many people have the same questions in mind and might now feel emboldened to follow up with their own questions. You ask many questions. Let me answer them in an order where my later answers build on earlier ones. I have a policy of discussing just one topic in a reply. This makes it easy for people to follow just the threads that interest them. So I will now give you several separate replies. If you want to follow up one of my replies, please reply directly to my reply so that we build a deep thread on one topic. But feel free to start off a new original post if you want to start a new topic or you want to recombine threads.

[@transmathematica]

The real numbers and number systems built on them are defined with just two operations - addition and multiplication. Subtraction and division are provided by auxiliary definitions. There are many different kinds of subtraction and division. The most widely used definition of subtraction ensures us that x - x = 0. This form of subtraction is called the additive inverse. Compare with Axiom 8 of transreal arithmetic: www.doi.org/10.1117/12.698153 Another definition of subtraction, usually called monus, agrees with the additive inverse where the result is zero or positive but returns zero wherever the additive inverse would return a negative number. Monus is used in number theory, abstract algebra, and computer proof systems. The situation is similar with division but there are many more varieties of division. The most widely used definition of division assures us that a x a^(-1) = 1 when a is non-zero. This is says: “a” times “a” to the power minus one, is equal to 1. It is known as the multiplicative inverse. Compare this with Axiom 18 of transreal arithmetic. Many other forms of division sometimes give answers that agree with the multiplicative inverse and sometimes disagree. Here are a few examples. I’ll write them out in words, because I am very restricted in the symbols I can use in a reply. Example: seven divided by two equals three remainder one. This form of division, called division with remainder, agrees with the multiplicative inverse when the remainder is zero and disagrees otherwise. It is used to provide excessively accurate numerical solutions to equations, often using the Chinese Remainder Theorem. It is used to find highest common factors. It is used in number theory. I am curious to know. Timpani112 and any readers, did you learn division with remainder in primary school? Example: seven divided by two equals three. This form of division is known as integer division. It is like division with remainder, except that the remainder is discarded. It is used to calculate intermediate results in long division algorithms, including algorithms for the division of polynomials. It is also used in computer hardware and software. I am curious to know. Timpani112 and any readers, did you learn long division in primary school? Transreal division is yet another form of division. It agrees with the multiplicative inverse when dividing by a non-zero number and provides an answer, on dividing by zero, where the multiplicative inverse gives no answer. Transreal division is multiplication by a certain kind of reciprocal. Check out the School playlist. It will take me a few weeks to work up to division, but you won’t have too long to wait. If you are in a real hurry, read the axioms of transreal arithmetic. In later answers, I will tell you some of the practical uses of transreal division.

[@transmathematica]

Error handling in computers is an important application of total systems, such as transreal arithmetic, but there are many more ways to handle errors. Check out the Evangelist playlist. Someone has agreed to be interviewed by me on the topic to totally exception-safe programming, but it will probably take a while to pin them down. Such is life! Transreal arithmetic extends all elementary real and complex functions so, for example, it is possible to solve trigonometric equations at singularities. link.springer.com/chapter/10.1007%2F978-94-017-7236-5_15 www.iaeng.org/publication/WCE2016/WCE2016_pp164-169.pdf As a curious example: cos^2(x) + sin^2(x) = 1^x, for all transreal x, including x equal to each of negative infinity, positive infinity, and nullity. I will definitely make a video on this! And I will make one on non-finite angles, but it will take a while to get round to these in the School playlist. If you are in a hurry, check out the above links and the papers they link to. Transreal arithmetic extends real calculus so that it is possible to obtain the value of a function, its derivatives and integrals, exactly at a singularity. If the value of the function at a singularity is equal to the limit that asymptotes to the singularity, then the function is continuous at the singularity, otherwise it is discontinuous at the singularity. This is exploited in the next application. Newton’s laws of motion are extended by transreal arithmetic so that they operate at singularities: dialnet.unirioja.es/descarga/articulo/6356671.pdf It is now possible to solve some physical problems exactly at singularities. Research is currently going on into extending the whole of complex calculus. Some results have been obtained in vector algebra and quaternions. This is enough to make transmathematicians confident, but not certain, that the whole of mathematical physics can be extended so that it operates exactly at singularities, in addition to working in the approach to singularities, as it does now.

[@transmathematica]

timpani112, Don't beat yourself up if you cannot see how to apply transmathematics right now. It takes a while to adapt to a new paradigm. I suggest you subscribe to the Transmathematica channel and work through the School playlist. This will give you an opportunity to learn transmathematics. You will also see applications of transreal arithmetic, and some other total arithmetics, in the Rehab, Evangelist, and Professional playlists. These might give you ideas on how to apply transmathematics in problems that interest you. I plan to publish a video every Friday. If I have more than one video ready to be published in a week, I will publish them on successive days. This week I published a video on Thursday so that I can experiment with how important social media is to my channel viewer metrics.

[@transmathematica]

timpani112, I have made strong claims about how transmathemtics can solve a wide range of problems from primary school arithmetic to topics in advanced research. I have backed up all of my claims with evidence. Conjectures are a different matter. There has been no movement on some of my conjectures, others have been confirmed, none has been refuted. timpani112 or any reader, if you think any of my claims have not been at least partially substantiated, then please post a reply so I can see what may remain to be done. This is not a promise to work on problems you highlight. I have a very clear view on my priorities for transmathematics. Other transmathematicians are similarly engaged on their personal research programmes. However, it does help us to know what people think about research in transmathematics and the transciences, so please do keep on commenting on these videos.