Apparently, the common sense on the division by zero with a long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on derivatives we have a great missing since $\tan (\pi/2) = 0$. Our mathematics is also wrong in elementary mathematics on the division by zero.
I wrote a simple draft on our division by zero. The contents are elementary and have wide connections to various fields beyond mathematics. I expect you write some philosophy, papers and essays on the division by zero from the attached source.
With best regards, Sincerely yours, Saburou Saitoh
The division by zero is uniquely and reasonably determined as 1/0=0/0=z/0=0 in the natural extensions of fractions. We have to change our basic ideas for our space and world
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/division%20by%20zero/announcement%20326-%20the%20divi http://okmr.yamatoblog.net/
Relations of 0 and infinity Hiroshi Okumura, Saburou Saitoh and Tsutomu Matsuura: http://www.e-jikei.org/…/Camera%20ready%20manuscript_JTSS_A… https://sites.google.com/site/sandrapinelas/icddea-2017 我々の初等数学には 間違いと欠陥がある。 学部程度の数学は 相当に変更されるべきである。 しかしながら、ゼロ除算の真実を知れば、人間は 人間の愚かさ、人間が如何に予断と偏見、思い込みに囚われた存在であるかを知ることが出来るだろう。この意味で、ゼロ除算は 人間開放に寄与するだろう。世界、社会が混乱を続けているのは、人間の無智の故であると言える。