Thank you for your kind information on Euler. Many mathematicians consider the division by zero 1/0 by the idea of continuity (by the limiting), however, the very important fact is the strong discontinuity at the origin. For the division by zero, I think the result is determined completely by the uniqueness theorem by Takahasi, the Yamada field structure and others. We gave many and many evidences. We have a serious mistake for the idea of the point at infinity; it is represented by zero, not infinity. The division by zero calculus has indeed many applications like l'Hospital. We have more three manuscripts, however, I think we had published enough papers already for the division by zero. The definition of the division by zero for many variable functions will be a very interesting problem. Please look the prototype example attached.
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Division by Zero z/0 = 0 in Euclidean Spaces Hiroshi Michiwaki, Hiroshi Okumura and Saburou Saitoh International Journal of Mathematics and Computation Vol. 28(2017); Issue 1, 2017), 1-16. http://www.scirp.org/journal/alamt http://dx.doi.org/10.4236/alamt.2016.62007 http://www.ijapm.org/show-63-504-1.html http://www.diogenes.bg/ijam/contents/2014-27-2/9/9.pdf http://okmr.yamatoblog.net/…/announcement%20326-%20the%20di… Announcement 326: The division by zero z/0=0/0=0 - its impact to human beings through education and research Qian,T./Rodino,L.(eds.): Mathematical Analysis, Probability and Applications -Plenary Lectures: Isaac 2015, Macau, China.