PR
Keyword Search
▼キーワード検索
再生核研究所
再生核研究所声明
Calendar
Comments
Freepage List
2017.01.22
カテゴリ： カテゴリ未分類
{\bf Fundamental open problem}: Give the definition of the division by zero calculus for multiply-valued functions with singularities,
\medskip
In order to make clear the problem, we shall give a prototype example.
We have the identity by the divison by zero calculus:
\begin{equation}
f(z) = \frac{1 + z}{1- z} =-1 , \quad \text{at} \quad z = 1.
\end{equation}
By the real part and imaginary part of the function, we have for $ z= x +iy$
\begin{equation}
\frac{1 - x^2 - y^2}{(1 - x)^2 + y^2} =-1, \quad \text{at}\quad (1,0)
\end{equation}
and
\begin{equation}
\frac{y}{(1- x)^2 + y^2} = 0, \quad \text{at}\quad (1,0),
\end{equation}
respectively. Why the differences happen? In general, we are interested in the above open question. Recall our definition for the division by zero calculus.
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/…/announcement%20326-%20the%20di…
Announcement 326: The division by zero z/0=0/0=0 - its impact to human beings through education and research
\medskip
In order to make clear the problem, we shall give a prototype example.
We have the identity by the divison by zero calculus:
\begin{equation}
f(z) = \frac{1 + z}{1- z} =-1 , \quad \text{at} \quad z = 1.
\end{equation}
By the real part and imaginary part of the function, we have for $ z= x +iy$
\begin{equation}
\frac{1 - x^2 - y^2}{(1 - x)^2 + y^2} =-1, \quad \text{at}\quad (1,0)
\end{equation}
and
\begin{equation}
\frac{y}{(1- x)^2 + y^2} = 0, \quad \text{at}\quad (1,0),
\end{equation}
respectively. Why the differences happen? In general, we are interested in the above open question. Recall our definition for the division by zero calculus.
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/…/announcement%20326-%20the%20di…
Announcement 326: The division by zero z/0=0/0=0 - its impact to human beings through education and research
お気に入りの記事を「いいね！」で応援しよう
Last updated
2017.01.22 15:38:26
【毎日開催】
15記事にいいね！で1ポイント
© Rakuten Group, Inc.
